LMFDB - Embedded newform 847.2.f.x.372.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.2
Root			$-0.206962 + 0.636964i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.x.148.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.206962 + 0.636964i) q^{2} +(-2.54013 + 1.84551i) q^{3} +(1.25514 + 0.911915i) q^{4} +(0.662464 + 2.03885i) q^{5} +(-0.649815 - 1.99992i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.92429 + 1.39808i) q^{8} +(2.11929 - 6.52251i) q^{9} +O(q^{10})$	\(q+(-0.206962 + 0.636964i) q^{2} +(-2.54013 + 1.84551i) q^{3} +(1.25514 + 0.911915i) q^{4} +(0.662464 + 2.03885i) q^{5} +(-0.649815 - 1.99992i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.92429 + 1.39808i) q^{8} +(2.11929 - 6.52251i) q^{9} -1.43578 q^{10} -4.87118 q^{12} +(-0.781276 + 2.40452i) q^{13} +(-0.541834 + 0.393666i) q^{14} +(-5.44548 - 3.95637i) q^{15} +(0.466573 + 1.43596i) q^{16} +(0.553425 + 1.70327i) q^{17} +(3.71599 + 2.69983i) q^{18} +(-5.44258 + 3.95427i) q^{19} +(-1.02778 + 3.16317i) q^{20} -3.13977 q^{21} -3.16429 q^{23} +(2.30778 - 7.10261i) q^{24} +(0.327016 - 0.237591i) q^{25} +(-1.36990 - 0.995290i) q^{26} +(3.74337 + 11.5209i) q^{27} +(0.479422 + 1.47551i) q^{28} +(-0.747669 - 0.543213i) q^{29} +(3.64707 - 2.64975i) q^{30} +(0.927602 - 2.85487i) q^{31} -5.76834 q^{32} -1.19946 q^{34} +(-0.662464 + 2.03885i) q^{35} +(8.60800 - 6.25408i) q^{36} +(1.21933 + 0.885898i) q^{37} +(-1.39232 - 4.28511i) q^{38} +(-2.45303 - 7.54965i) q^{39} +(-4.12526 - 2.99718i) q^{40} +(4.49897 - 3.26870i) q^{41} +(0.649815 - 1.99992i) q^{42} +8.42985 q^{43} +14.7024 q^{45} +(0.654888 - 2.01554i) q^{46} +(-3.55782 + 2.58491i) q^{47} +(-3.83525 - 2.78647i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.0836570 + 0.257470i) q^{50} +(-4.54917 - 3.30516i) q^{51} +(-3.17333 + 2.30556i) q^{52} +(0.206244 - 0.634755i) q^{53} -8.11314 q^{54} -2.37856 q^{56} +(6.52722 - 20.0887i) q^{57} +(0.500747 - 0.363814i) q^{58} +(0.298010 + 0.216517i) q^{59} +(-3.22698 - 9.93163i) q^{60} +(-1.54863 - 4.76621i) q^{61} +(1.62647 + 1.18170i) q^{62} +(5.54838 - 4.03113i) q^{63} +(0.260682 - 0.802296i) q^{64} -5.42003 q^{65} -0.902129 q^{67} +(-0.858607 + 2.64252i) q^{68} +(8.03770 - 5.83973i) q^{69} +(-1.16157 - 0.843932i) q^{70} +(-4.59489 - 14.1416i) q^{71} +(5.04086 + 15.5142i) q^{72} +(6.50301 + 4.72471i) q^{73} +(-0.816641 + 0.593325i) q^{74} +(-0.392186 + 1.20702i) q^{75} -10.4372 q^{76} +5.31654 q^{78} +(-1.25358 + 3.85813i) q^{79} +(-2.61863 + 1.90255i) q^{80} +(-14.1255 - 10.2628i) q^{81} +(1.15092 + 3.54218i) q^{82} +(1.25193 + 3.85305i) q^{83} +(-3.94087 - 2.86321i) q^{84} +(-3.10609 + 2.25670i) q^{85} +(-1.74466 + 5.36951i) q^{86} +2.90168 q^{87} -8.30727 q^{89} +(-3.04284 + 9.36491i) q^{90} +(-2.04541 + 1.48608i) q^{91} +(-3.97163 - 2.88556i) q^{92} +(2.91246 + 8.96363i) q^{93} +(-0.910159 - 2.80118i) q^{94} +(-11.6677 - 8.47707i) q^{95} +(14.6523 - 10.6455i) q^{96} +(2.63154 - 8.09904i) q^{97} -0.669744 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.206962	+	0.636964i	−0.146344	+	0.450402i	−0.997181	−	0.0750279i	$-0.976095\pi$
$2$	−0.206962	+	0.636964i	−0.146344	+	0.450402i	0.850837	+	0.525430i	$0.176095\pi$
$3$	−2.54013	+	1.84551i	−1.46654	+	1.06551i	−0.484948	+	0.874543i	$0.661161\pi$
$3$	−2.54013	+	1.84551i	−1.46654	+	1.06551i	−0.981597	+	0.190964i	$0.938839\pi$
$4$	1.25514	+	0.911915i	0.627572	+	0.455958i
$5$	0.662464	+	2.03885i	0.296263	+	0.911803i	0.982794	+	0.184703i	$0.0591324\pi$
$5$	0.662464	+	2.03885i	0.296263	+	0.911803i	−0.686531	+	0.727100i	$0.740868\pi$
$6$	−0.649815	−	1.99992i	−0.265286	−	0.816465i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−1.92429	+	1.39808i	−0.680340	+	0.494296i
$9$	2.11929	−	6.52251i	0.706431	−	2.17417i
$10$	−1.43578			−0.454034
$11$		0			0
$11$		0			0
$12$	−4.87118			−1.40619
$13$	−0.781276	+	2.40452i	−0.216687	+	0.666894i	0.782343	+	0.622848i	$0.214025\pi$
$13$	−0.781276	+	2.40452i	−0.216687	+	0.666894i	−0.999030	+	0.0440455i	$0.985975\pi$
$14$	−0.541834	+	0.393666i	−0.144811	+	0.105212i
$15$	−5.44548	−	3.95637i	−1.40602	−	1.02153i
$16$	0.466573	+	1.43596i	0.116643	+	0.358991i
$17$	0.553425	+	1.70327i	0.134225	+	0.413103i	0.995469	−	0.0950899i	$-0.0303138\pi$
$17$	0.553425	+	1.70327i	0.134225	+	0.413103i	−0.861244	+	0.508193i	$0.830314\pi$
$18$	3.71599	+	2.69983i	0.875868	+	0.636356i
$19$	−5.44258	+	3.95427i	−1.24861	+	0.907171i	−0.998141	−	0.0609525i	$-0.980586\pi$
$19$	−5.44258	+	3.95427i	−1.24861	+	0.907171i	−0.250473	+	0.968124i	$0.580586\pi$
$20$	−1.02778	+	3.16317i	−0.229818	+	0.707306i
$21$	−3.13977			−0.685155
$22$		0			0
$23$	−3.16429			−0.659799			−0.329900	−	0.944016i	$-0.607015\pi$
$23$	−3.16429			−0.659799			−0.329900	+	0.944016i	$0.607015\pi$
$24$	2.30778	−	7.10261i	0.471073	−	1.44982i
$25$	0.327016	−	0.237591i	0.0654031	−	0.0475182i
$26$	−1.36990	−	0.995290i	−0.268659	−	0.195192i
$27$	3.74337	+	11.5209i	0.720412	+	2.21720i
$28$	0.479422	+	1.47551i	0.0906023	+	0.278845i
$29$	−0.747669	−	0.543213i	−0.138839	−	0.100872i	0.516198	−	0.856469i	$-0.327347\pi$
$29$	−0.747669	−	0.543213i	−0.138839	−	0.100872i	−0.655037	+	0.755597i	$0.727347\pi$
$30$	3.64707	−	2.64975i	0.665862	−	0.483777i
$31$	0.927602	−	2.85487i	0.166602	−	0.512749i	−0.832549	−	0.553952i	$-0.813119\pi$
$31$	0.927602	−	2.85487i	0.166602	−	0.512749i	0.999151	+	0.0412031i	$0.0131191\pi$
$32$	−5.76834			−1.01971
$33$		0			0
$34$	−1.19946			−0.205705
$35$	−0.662464	+	2.03885i	−0.111977	+	0.344629i
$36$	8.60800	−	6.25408i	1.43467	−	1.04235i
$37$	1.21933	+	0.885898i	0.200457	+	0.145641i	0.683486	−	0.729964i	$-0.260463\pi$
$37$	1.21933	+	0.885898i	0.200457	+	0.145641i	−0.483028	+	0.875605i	$0.660463\pi$
$38$	−1.39232	−	4.28511i	−0.225864	−	0.695137i
$39$	−2.45303	−	7.54965i	−0.392799	−	1.20891i
$40$	−4.12526	−	2.99718i	−0.652261	−	0.473895i
$41$	4.49897	−	3.26870i	0.702622	−	0.510485i	−0.178163	−	0.984001i	$-0.557016\pi$
$41$	4.49897	−	3.26870i	0.702622	−	0.510485i	0.880785	+	0.473516i	$0.157016\pi$
$42$	0.649815	−	1.99992i	0.100269	−	0.308595i
$43$	8.42985			1.28554			0.642770	−	0.766059i	$-0.277785\pi$
$43$	8.42985			1.28554			0.642770	+	0.766059i	$0.277785\pi$
$44$		0			0
$45$	14.7024			2.19171
$46$	0.654888	−	2.01554i	0.0965579	−	0.297175i
$47$	−3.55782	+	2.58491i	−0.518961	+	0.377047i	−0.816212	−	0.577752i	$-0.803930\pi$
$47$	−3.55782	+	2.58491i	−0.518961	+	0.377047i	0.297251	+	0.954799i	$0.403930\pi$
$48$	−3.83525	−	2.78647i	−0.553570	−	0.402192i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.0836570	+	0.257470i	0.0118309	+	0.0364117i
$51$	−4.54917	−	3.30516i	−0.637011	−	0.462816i
$52$	−3.17333	+	2.30556i	−0.440062	+	0.319724i
$53$	0.206244	−	0.634755i	0.0283298	−	0.0871903i	−0.935892	−	0.352287i	$-0.885404\pi$
$53$	0.206244	−	0.634755i	0.0283298	−	0.0871903i	0.964222	+	0.265097i	$0.0854040\pi$
$54$	−8.11314			−1.10406
$55$		0			0
$56$	−2.37856			−0.317848
$57$	6.52722	−	20.0887i	0.864551	−	2.66081i
$58$	0.500747	−	0.363814i	0.0657513	−	0.0477711i
$59$	0.298010	+	0.216517i	0.0387976	+	0.0281881i	0.607015	−	0.794690i	$-0.292367\pi$
$59$	0.298010	+	0.216517i	0.0387976	+	0.0281881i	−0.568217	+	0.822878i	$0.692367\pi$
$60$	−3.22698	−	9.93163i	−0.416601	−	1.28217i
$61$	−1.54863	−	4.76621i	−0.198282	−	0.610250i	−0.999923	−	0.0124435i	$-0.996039\pi$
$61$	−1.54863	−	4.76621i	−0.198282	−	0.610250i	0.801640	−	0.597807i	$-0.203961\pi$
$62$	1.62647	+	1.18170i	0.206562	+	0.150076i
$63$	5.54838	−	4.03113i	0.699030	−	0.507875i
$64$	0.260682	−	0.802296i	0.0325852	−	0.100287i
$65$	−5.42003			−0.672273
$66$		0			0
$67$	−0.902129			−0.110213			−0.0551063	−	0.998480i	$-0.517550\pi$
$67$	−0.902129			−0.110213			−0.0551063	+	0.998480i	$0.517550\pi$
$68$	−0.858607	+	2.64252i	−0.104121	+	0.320453i
$69$	8.03770	−	5.83973i	0.967625	−	0.703021i
$70$	−1.16157	−	0.843932i	−0.138834	−	0.100869i
$71$	−4.59489	−	14.1416i	−0.545313	−	1.67830i	−0.720245	−	0.693720i	$-0.755971\pi$
$71$	−4.59489	−	14.1416i	−0.545313	−	1.67830i	0.174932	−	0.984580i	$-0.444029\pi$
$72$	5.04086	+	15.5142i	0.594071	+	1.82836i
$73$	6.50301	+	4.72471i	0.761119	+	0.552986i	0.899254	−	0.437428i	$-0.144110\pi$
$73$	6.50301	+	4.72471i	0.761119	+	0.552986i	−0.138134	+	0.990414i	$0.544110\pi$
$74$	−0.816641	+	0.593325i	−0.0949326	+	0.0689726i
$75$	−0.392186	+	1.20702i	−0.0452857	+	0.139375i
$76$	−10.4372			−1.19723
$77$		0			0
$78$	5.31654			0.601980
$79$	−1.25358	+	3.85813i	−0.141039	+	0.434074i	−0.996480	−	0.0838261i	$-0.973286\pi$
$79$	−1.25358	+	3.85813i	−0.141039	+	0.434074i	0.855441	+	0.517900i	$0.173286\pi$
$80$	−2.61863	+	1.90255i	−0.292772	+	0.212711i
$81$	−14.1255	−	10.2628i	−1.56950	−	1.14031i
$82$	1.15092	+	3.54218i	0.127098	+	0.391169i
$83$	1.25193	+	3.85305i	0.137418	+	0.422928i	0.995958	−	0.0898178i	$-0.0286285\pi$
$83$	1.25193	+	3.85305i	0.137418	+	0.422928i	−0.858541	+	0.512745i	$0.828628\pi$
$84$	−3.94087	−	2.86321i	−0.429984	−	0.312402i
$85$	−3.10609	+	2.25670i	−0.336902	+	0.244774i
$86$	−1.74466	+	5.36951i	−0.188132	+	0.579009i
$87$	2.90168			0.311093
$88$		0			0
$89$	−8.30727			−0.880569			−0.440284	−	0.897858i	$-0.645122\pi$
$89$	−8.30727			−0.880569			−0.440284	+	0.897858i	$0.645122\pi$
$90$	−3.04284	+	9.36491i	−0.320744	+	0.987148i
$91$	−2.04541	+	1.48608i	−0.214417	+	0.155783i
$92$	−3.97163	−	2.88556i	−0.414071	−	0.300840i
$93$	2.91246	+	8.96363i	0.302008	+	0.929485i
$94$	−0.910159	−	2.80118i	−0.0938758	−	0.288920i
$95$	−11.6677	−	8.47707i	−1.19708	−	0.869729i
$96$	14.6523	−	10.6455i	1.49545	−	1.08651i
$97$	2.63154	−	8.09904i	0.267192	−	0.822333i	−0.723988	−	0.689812i	$-0.757693\pi$
$97$	2.63154	−	8.09904i	0.267192	−	0.822333i	0.991180	−	0.132520i	$-0.0423070\pi$
$98$	−0.669744			−0.0676544
$99$		0			0
$100$	0.627115			0.0627115
$101$	1.24443	−	3.82997i	0.123826	−	0.381096i	−0.869860	−	0.493299i	$-0.835791\pi$
$101$	1.24443	−	3.82997i	0.123826	−	0.381096i	0.993685	+	0.112203i	$0.0357907\pi$
$102$	3.04678	−	2.21361i	0.301676	−	0.219180i
$103$	14.2596	+	10.3602i	1.40504	+	1.02082i	0.994020	+	0.109195i	$0.0348272\pi$
$103$	14.2596	+	10.3602i	1.40504	+	1.02082i	0.411020	+	0.911626i	$0.365173\pi$
$104$	−1.85831	−	5.71929i	−0.182222	−	0.560822i
$105$	−2.07999	−	6.40154i	−0.202986	−	0.624726i
$106$	0.361631	+	0.262741i	0.0351248	+	0.0255196i
$107$	−12.4619	+	9.05408i	−1.20473	+	0.875291i	−0.994742	−	0.102412i	$-0.967344\pi$
$107$	−12.4619	+	9.05408i	−1.20473	+	0.875291i	−0.209993	+	0.977703i	$0.567344\pi$
$108$	−5.80762	+	17.8740i	−0.558839	+	1.71993i
$109$	18.9265			1.81283			0.906416	−	0.422386i	$-0.138807\pi$
$109$	18.9265			1.81283			0.906416	+	0.422386i	$0.138807\pi$
$110$		0			0
$111$	−4.73220			−0.449161
$112$	−0.466573	+	1.43596i	−0.0440870	+	0.135686i
$113$	−1.35965	+	0.987844i	−0.127905	+	0.0929286i	−0.649898	−	0.760021i	$-0.725189\pi$
$113$	−1.35965	+	0.987844i	−0.127905	+	0.0929286i	0.521993	+	0.852950i	$0.325189\pi$
$114$	11.4449	+	8.31521i	1.07191	+	0.778790i
$115$	−2.09623	−	6.45152i	−0.195474	−	0.601607i
$116$	−0.443068	−	1.36362i	−0.0411378	−	0.126609i
$117$	14.0278	+	10.1918i	1.29687	+	0.942229i
$118$	−0.199590	+	0.145011i	−0.0183738	+	0.0133493i
$119$	−0.553425	+	1.70327i	−0.0507324	+	0.156138i
$120$	16.0100			1.46151
$121$		0			0
$122$	3.35641			0.303875
$123$	−5.39556	+	16.6058i	−0.486501	+	1.49730i
$124$	3.76767	−	2.73737i	0.338347	−	0.245823i
$125$	9.37282	+	6.80975i	0.838330	+	0.609082i
$126$	1.41938	+	4.36841i	0.126449	+	0.389169i
$127$	−5.42848	−	16.7071i	−0.481699	−	1.48252i	−0.836705	−	0.547654i	$-0.815521\pi$
$127$	−5.42848	−	16.7071i	−0.481699	−	1.48252i	0.355006	−	0.934864i	$-0.384479\pi$
$128$	−8.87628	−	6.44900i	−0.784560	−	0.570016i
$129$	−21.4129	+	15.5574i	−1.88530	+	1.36975i
$130$	1.12174	−	3.45237i	0.0983833	−	0.302793i
$131$	−6.72557			−0.587616			−0.293808	−	0.955865i	$-0.594923\pi$
$131$	−6.72557			−0.587616			−0.293808	+	0.955865i	$0.594923\pi$
$132$		0			0
$133$	−6.72740			−0.583340
$134$	0.186707	−	0.574624i	0.0161290	−	0.0496400i
$135$	−21.0096	+	15.2644i	−1.80822	+	1.31375i
$136$	−3.44625	−	2.50385i	−0.295514	−	0.214703i
$137$	4.28533	+	13.1889i	0.366121	+	1.12680i	0.949276	+	0.314443i	$0.101818\pi$
$137$	4.28533	+	13.1889i	0.366121	+	1.12680i	−0.583156	+	0.812360i	$0.698182\pi$
$138$	2.05620	+	6.32833i	0.175035	+	0.538703i
$139$	11.5453	+	8.38812i	0.979256	+	0.711471i	0.957542	−	0.288293i	$-0.0930877\pi$
$139$	11.5453	+	8.38812i	0.979256	+	0.711471i	0.0217140	+	0.999764i	$0.493088\pi$
$140$	−2.69075	+	1.95494i	−0.227410	+	0.165223i
$141$	4.26685	−	13.1320i	0.359333	−	1.10591i
$142$	9.95867			0.835713
$143$		0			0
$144$	10.3549			0.862908
$145$	0.612229	−	1.88425i	0.0508429	−	0.156478i
$146$	−4.35535	+	3.16435i	−0.360451	+	0.261883i
$147$	−2.54013	−	1.84551i	−0.209506	−	0.152215i
$148$	0.722575	+	2.22386i	0.0593953	+	0.182800i
$149$	−0.810527	−	2.49455i	−0.0664010	−	0.204361i	0.912351	−	0.409409i	$-0.134265\pi$
$149$	−0.810527	−	2.49455i	−0.0664010	−	0.204361i	−0.978752	+	0.205048i	$0.934265\pi$
$150$	−0.687663	−	0.499616i	−0.0561475	−	0.0407935i
$151$	−2.41864	+	1.75724i	−0.196826	+	0.143002i	−0.681833	−	0.731508i	$-0.738817\pi$
$151$	−2.41864	+	1.75724i	−0.196826	+	0.143002i	0.485007	+	0.874510i	$0.338817\pi$
$152$	4.94474	−	15.2183i	0.401071	−	1.23437i
$153$	12.2824			0.992977
$154$		0			0
$155$	6.43516			0.516884
$156$	3.80574	−	11.7128i	0.304703	−	0.937779i
$157$	−9.10524	+	6.61534i	−0.726677	+	0.527962i	−0.888511	−	0.458856i	$-0.848259\pi$
$157$	−9.10524	+	6.61534i	−0.726677	+	0.527962i	0.161833	+	0.986818i	$0.448259\pi$
$158$	−2.19805	−	1.59698i	−0.174867	−	0.127049i
$159$	0.647561	+	1.99299i	0.0513549	+	0.158054i
$160$	−3.82131	−	11.7608i	−0.302101	−	0.929773i
$161$	−2.55996	−	1.85992i	−0.201753	−	0.146582i
$162$	9.46045	−	6.87342i	0.743283	−	0.540027i
$163$	−5.62502	+	17.3120i	−0.440586	+	1.35598i	0.446667	+	0.894700i	$0.352611\pi$
$163$	−5.62502	+	17.3120i	−0.440586	+	1.35598i	−0.887253	+	0.461283i	$0.847389\pi$
$164$	8.62763			0.673705
$165$		0			0
$166$	−2.71336			−0.210598
$167$	−6.15909	+	18.9557i	−0.476605	+	1.46684i	0.367176	+	0.930151i	$0.380325\pi$
$167$	−6.15909	+	18.9557i	−0.476605	+	1.46684i	−0.843781	+	0.536687i	$0.819675\pi$
$168$	6.04184	−	4.38966i	0.466138	−	0.338669i
$169$	5.34590	+	3.88402i	0.411223	+	0.298771i
$170$	−0.794597	−	2.44552i	−0.0609428	−	0.187563i
$171$	14.2573	+	43.8796i	1.09029	+	3.35555i
$172$	10.5807	+	7.68731i	0.806769	+	0.586152i
$173$	4.84607	−	3.52088i	0.368440	−	0.267687i	−0.388124	−	0.921607i	$-0.626877\pi$
$173$	4.84607	−	3.52088i	0.368440	−	0.267687i	0.756564	+	0.653920i	$0.226877\pi$
$174$	−0.600539	+	1.84827i	−0.0455267	+	0.140117i
$175$	0.404214			0.0305557
$176$		0			0
$177$	−1.15657			−0.0869329
$178$	1.71929	−	5.29143i	0.128866	−	0.396610i
$179$	1.30975	−	0.951588i	0.0978952	−	0.0711251i	−0.537761	−	0.843097i	$-0.680730\pi$
$179$	1.30975	−	0.951588i	0.0978952	−	0.0711251i	0.635656	+	0.771972i	$0.280730\pi$
$180$	18.4536	+	13.4074i	1.37545	+	0.999325i
$181$	0.749929	+	2.30804i	0.0557418	+	0.171556i	0.975051	−	0.221980i	$-0.0712519\pi$
$181$	0.749929	+	2.30804i	0.0557418	+	0.171556i	−0.919309	+	0.393535i	$0.871252\pi$
$182$	−0.523255	−	1.61041i	−0.0387862	−	0.119372i
$183$	12.7298	+	9.24876i	0.941016	+	0.683688i
$184$	6.08901	−	4.42393i	0.448888	−	0.326136i
$185$	−0.998452	+	3.07292i	−0.0734077	+	0.225926i
$186$	−6.31228			−0.462839
$187$		0			0
$188$	−6.82279			−0.497603
$189$	−3.74337	+	11.5209i	−0.272290	+	0.838023i
$190$	7.81436	−	5.67747i	0.566914	−	0.411887i
$191$	−10.2753	−	7.46541i	−0.743492	−	0.540178i	0.150311	−	0.988639i	$-0.451973\pi$
$191$	−10.2753	−	7.46541i	−0.743492	−	0.540178i	−0.893803	+	0.448460i	$0.851973\pi$
$192$	0.818481	+	2.51903i	0.0590688	+	0.181795i
$193$	0.543657	+	1.67320i	0.0391333	+	0.120440i	0.968715	−	0.248177i	$-0.0798314\pi$
$193$	0.543657	+	1.67320i	0.0391333	+	0.120440i	−0.929581	+	0.368617i	$0.879831\pi$
$194$	4.61417	+	3.35239i	0.331278	+	0.240688i
$195$	13.7676	−	10.0027i	0.985918	−	0.716311i
$196$	−0.479422	+	1.47551i	−0.0342444	+	0.105394i
$197$	0.903053			0.0643399			0.0321699	−	0.999482i	$-0.489758\pi$
$197$	0.903053			0.0643399			0.0321699	+	0.999482i	$0.489758\pi$
$198$		0			0
$199$	−15.6296			−1.10795			−0.553976	−	0.832533i	$-0.686890\pi$
$199$	−15.6296			−1.10795			−0.553976	+	0.832533i	$0.686890\pi$
$200$	−0.297103	+	0.914389i	−0.0210084	+	0.0646571i
$201$	2.29153	−	1.66489i	0.161632	−	0.117432i
$202$	2.18200	+	1.58532i	0.153525	+	0.111543i
$203$	−0.285584	−	0.878938i	−0.0200441	−	0.0616893i
$204$	−2.69583	−	8.29691i	−0.188746	−	0.580900i
$205$	9.64480	+	7.00736i	0.673622	+	0.489415i
$206$	−9.55028	+	6.93868i	−0.665399	+	0.483441i
$207$	−6.70605	+	20.6391i	−0.466103	+	1.43452i
$208$	−3.81733			−0.264684
$209$		0			0
$210$	4.50803			0.311084
$211$	−4.56378	+	14.0459i	−0.314184	+	0.966958i	0.661905	+	0.749587i	$0.269748\pi$
$211$	−4.56378	+	14.0459i	−0.314184	+	0.966958i	−0.976089	+	0.217371i	$0.930252\pi$
$212$	0.837709	−	0.608631i	0.0575341	−	0.0418010i
$213$	37.7701	+	27.4416i	2.58797	+	1.88027i
$214$	−3.18799	−	9.81162i	−0.217926	−	0.670709i
$215$	5.58447	+	17.1872i	0.380858	+	1.17216i
$216$	−23.3105	−	16.9361i	−1.58608	−	1.15235i
$217$	2.42849	−	1.76440i	0.164857	−	0.119776i
$218$	−3.91708	+	12.0555i	−0.265298	+	0.816503i
$219$	−25.2380			−1.70543
$220$		0			0
$221$	−4.52791			−0.304581
$222$	0.979387	−	3.01424i	0.0657322	−	0.202303i
$223$	1.49293	−	1.08468i	0.0999743	−	0.0726356i	−0.536675	−	0.843789i	$-0.680320\pi$
$223$	1.49293	−	1.08468i	0.0999743	−	0.0726356i	0.636649	+	0.771153i	$0.280320\pi$
$224$	−4.66668	−	3.39054i	−0.311806	−	0.226540i
$225$	−0.856647	−	2.63649i	−0.0571098	−	0.175766i
$226$	−0.347825	−	1.07050i	−0.0231370	−	0.0712083i
$227$	−17.7498	−	12.8960i	−1.17809	−	0.855936i	−0.186139	−	0.982523i	$-0.559597\pi$
$227$	−17.7498	−	12.8960i	−1.17809	−	0.855936i	−0.991955	+	0.126588i	$0.959597\pi$
$228$	26.5118	−	19.2619i	1.75579	−	1.27565i
$229$	−6.25815	+	19.2606i	−0.413550	+	1.27278i	0.499991	+	0.866030i	$0.333337\pi$
$229$	−6.25815	+	19.2606i	−0.413550	+	1.27278i	−0.913541	+	0.406746i	$0.866663\pi$
$230$	4.54323			0.299571
$231$		0			0
$232$	2.19819			0.144318
$233$	−6.50870	+	20.0317i	−0.426399	+	1.31232i	0.475250	+	0.879851i	$0.342358\pi$
$233$	−6.50870	+	20.0317i	−0.426399	+	1.31232i	−0.901648	+	0.432470i	$0.857642\pi$
$234$	−9.39501	+	6.82587i	−0.614171	+	0.446221i
$235$	−7.62718	−	5.54147i	−0.497542	−	0.361486i
$236$	0.176600	+	0.543519i	0.0114957	+	0.0353801i
$237$	−3.93597	−	12.1137i	−0.255668	−	0.786867i
$238$	−0.970382	−	0.705023i	−0.0629005	−	0.0456999i
$239$	12.5370	−	9.10863i	0.810948	−	0.589188i	−0.103157	−	0.994665i	$-0.532894\pi$
$239$	12.5370	−	9.10863i	0.810948	−	0.589188i	0.914105	+	0.405477i	$0.132894\pi$
$240$	3.14049	−	9.66544i	0.202718	−	0.623902i
$241$	−14.0848			−0.907283			−0.453641	−	0.891184i	$-0.649875\pi$
$241$	−14.0848			−0.907283			−0.453641	+	0.891184i	$0.649875\pi$
$242$		0			0
$243$	18.4792			1.18544
$244$	2.40262	−	7.39450i	0.153812	−	0.473384i
$245$	−1.73435	+	1.26008i	−0.110804	+	0.0805036i
$246$	−9.46064	−	6.87356i	−0.603188	−	0.438242i
$247$	−5.25596	−	16.1762i	−0.334429	−	1.02927i
$248$	2.20635	+	6.79046i	0.140104	+	0.431195i
$249$	−10.2909	−	7.47680i	−0.652161	−	0.473823i
$250$	−6.27739	+	4.56079i	−0.397017	+	0.288450i
$251$	−0.332894	+	1.02454i	−0.0210121	+	0.0646686i	−0.961013	−	0.276504i	$-0.910824\pi$
$251$	−0.332894	+	1.02454i	−0.0210121	+	0.0646686i	0.940001	+	0.341173i	$0.110824\pi$
$252$	10.6401			0.670261
$253$		0			0
$254$	11.7653			0.738223
$255$	3.72509	−	11.4646i	0.233274	−	0.717944i
$256$	7.30978	−	5.31087i	0.456861	−	0.331929i
$257$	−10.5828	−	7.68883i	−0.660135	−	0.479616i	0.206574	−	0.978431i	$-0.433769\pi$
$257$	−10.5828	−	7.68883i	−0.660135	−	0.479616i	−0.866708	+	0.498815i	$0.833769\pi$
$258$	−5.47784	−	16.8591i	−0.341035	−	1.04960i
$259$	0.465744	+	1.43341i	0.0289399	+	0.0890679i
$260$	−6.80292	−	4.94261i	−0.421899	−	0.306528i
$261$	−5.12765	+	3.72545i	−0.317393	+	0.230600i
$262$	1.39194	−	4.28395i	0.0859943	−	0.264663i
$263$	9.57216			0.590245			0.295122	−	0.955459i	$-0.404640\pi$
$263$	9.57216			0.590245			0.295122	+	0.955459i	$0.404640\pi$
$264$		0			0
$265$	1.43080			0.0878935
$266$	1.39232	−	4.28511i	0.0853685	−	0.262737i
$267$	21.1015	−	15.3312i	1.29139	−	0.938252i
$268$	−1.13230	−	0.822665i	−0.0691663	−	0.0502523i
$269$	−1.47356	−	4.53514i	−0.0898444	−	0.276513i	0.896031	−	0.443991i	$-0.146438\pi$
$269$	−1.47356	−	4.53514i	−0.0898444	−	0.276513i	−0.985876	+	0.167478i	$0.946438\pi$
$270$	−5.37466	−	16.5415i	−0.327092	−	1.00668i
$271$	−16.2226	−	11.7864i	−0.985455	−	0.715975i	−0.0265341	−	0.999648i	$-0.508447\pi$
$271$	−16.2226	−	11.7864i	−0.985455	−	0.715975i	−0.958921	+	0.283673i	$0.908447\pi$
$272$	−2.18762	+	1.58940i	−0.132644	+	0.0963713i
$273$	2.45303	−	7.54965i	0.148464	−	0.456926i
$274$	−9.28776			−0.561094
$275$		0			0
$276$	15.4138			0.927802
$277$	3.58535	−	11.0346i	0.215423	−	0.663004i	−0.783700	−	0.621139i	$-0.786670\pi$
$277$	3.58535	−	11.0346i	0.215423	−	0.663004i	0.999123	−	0.0418647i	$-0.0133299\pi$
$278$	−7.73237	+	5.61789i	−0.463757	+	0.336939i
$279$	−16.6550	−	12.1006i	−0.997111	−	0.724443i
$280$	−1.57571	−	4.84953i	−0.0941666	−	0.289815i
$281$	−3.73256	−	11.4876i	−0.222666	−	0.685295i	−0.998520	−	0.0543830i	$-0.982681\pi$
$281$	−3.73256	−	11.4876i	−0.222666	−	0.685295i	0.775854	−	0.630912i	$-0.217319\pi$
$282$	7.48154	+	5.43566i	0.445519	+	0.323689i
$283$	17.7929	−	12.9273i	1.05768	−	0.768448i	0.0840200	−	0.996464i	$-0.473224\pi$
$283$	17.7929	−	12.9273i	1.05768	−	0.768448i	0.973657	+	0.228017i	$0.0732240\pi$
$284$	7.12871	−	21.9399i	0.423011	−	1.30189i
$285$	45.2820			2.68227
$286$		0			0
$287$	5.56104			0.328258
$288$	−12.2248	+	37.6240i	−0.720353	+	2.21702i
$289$	11.1585	−	8.10709i	0.656380	−	0.476888i
$290$	1.07349	+	0.779936i	0.0630375	+	0.0457994i
$291$	8.26243	+	25.4291i	0.484352	+	1.49068i
$292$	3.85367	+	11.8604i	0.225519	+	0.694077i
$293$	1.14654	+	0.833014i	0.0669819	+	0.0486652i	0.620772	−	0.783991i	$-0.286819\pi$
$293$	1.14654	+	0.833014i	0.0669819	+	0.0486652i	−0.553790	+	0.832656i	$0.686819\pi$
$294$	1.70124	−	1.23602i	0.0992181	−	0.0720862i
$295$	−0.244025	+	0.751033i	−0.0142077	+	0.0437268i
$296$	−3.58491			−0.208369
$297$		0			0
$298$	1.75669			0.101762
$299$	2.47218	−	7.60859i	0.142970	−	0.440016i
$300$	−1.59295	+	1.15735i	−0.0919691	+	0.0668195i
$301$	6.81989	+	4.95494i	0.393092	+	0.285598i
$302$	−0.618734	−	1.90427i	−0.0356041	−	0.109578i
$303$	3.90724	+	12.0252i	0.224465	+	0.690832i
$304$	−8.21755	−	5.97040i	−0.471309	−	0.342426i
$305$	8.69169	−	6.31488i	0.497685	−	0.361589i
$306$	−2.54200	+	7.82348i	−0.145317	+	0.447238i
$307$	−29.4646			−1.68163			−0.840817	−	0.541319i	$-0.817925\pi$
$307$	−29.4646			−1.68163			−0.840817	+	0.541319i	$0.817925\pi$
$308$		0			0
$309$	−55.3411			−3.14825
$310$	−1.33183	+	4.09897i	−0.0756431	+	0.232806i
$311$	−21.7453	+	15.7989i	−1.23306	+	0.895873i	−0.997116	−	0.0758927i	$-0.975819\pi$
$311$	−21.7453	+	15.7989i	−1.23306	+	0.895873i	−0.235948	+	0.971766i	$0.575819\pi$
$312$	15.2754	+	11.0982i	0.864797	+	0.628312i
$313$	−1.38832	−	4.27281i	−0.0784725	−	0.241514i	0.904123	−	0.427273i	$-0.140526\pi$
$313$	−1.38832	−	4.27281i	−0.0784725	−	0.241514i	−0.982595	+	0.185759i	$0.940526\pi$
$314$	−2.32930	−	7.16884i	−0.131450	−	0.404561i
$315$	11.8945	+	8.64186i	0.670179	+	0.486914i
$316$	−5.09172	+	3.69935i	−0.286431	+	0.208105i
$317$	−3.38376	+	10.4141i	−0.190051	+	0.584916i	−0.999999	−	0.00158586i	$-0.999495\pi$
$317$	−3.38376	+	10.4141i	−0.190051	+	0.584916i	0.809948	+	0.586502i	$0.199495\pi$
$318$	−1.40348			−0.0787034
$319$		0			0
$320$	1.80846			0.101096
$321$	14.9454	−	45.9971i	0.834169	−	2.56731i
$322$	1.71452	−	1.24567i	0.0955464	−	0.0694185i
$323$	−9.74723	−	7.08177i	−0.542350	−	0.394040i
$324$	−8.37074	−	25.7625i	−0.465041	−	1.43125i
$325$	0.315802	+	0.971940i	0.0175176	+	0.0539135i
$326$	−9.86298	−	7.16588i	−0.546260	−	0.396881i
$327$	−48.0758	+	34.9291i	−2.65860	+	1.93159i
$328$	−4.08744	+	12.5799i	−0.225691	+	0.694607i
$329$	−4.39771			−0.242453
$330$		0			0
$331$	16.5226			0.908166			0.454083	−	0.890959i	$-0.349967\pi$
$331$	16.5226			0.908166			0.454083	+	0.890959i	$0.349967\pi$
$332$	−1.94230	+	5.97779i	−0.106598	+	0.328074i
$333$	8.36241	−	6.07564i	0.458257	−	0.332943i
$334$	−10.7994	−	7.84624i	−0.590918	−	0.429327i
$335$	−0.597628	−	1.83931i	−0.0326519	−	0.100492i
$336$	−1.46493	−	4.50860i	−0.0799187	−	0.245964i
$337$	−9.80588	−	7.12439i	−0.534160	−	0.388090i	0.287751	−	0.957705i	$-0.407092\pi$
$337$	−9.80588	−	7.12439i	−0.534160	−	0.388090i	−0.821912	+	0.569615i	$0.807092\pi$
$338$	−3.58038	+	2.60130i	−0.194747	+	0.141492i
$339$	1.63061	−	5.01851i	0.0885626	−	0.272568i
$340$	−5.95651			−0.323037
$341$		0			0
$342$	−30.9004			−1.67090
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−16.2215	+	11.7856i	−0.874605	+	0.635437i
$345$	17.2310	+	12.5191i	0.927688	+	0.674005i
$346$	1.23972	+	3.81547i	0.0666478	+	0.205121i
$347$	7.50452	+	23.0965i	0.402864	+	1.23989i	0.922666	+	0.385600i	$0.126006\pi$
$347$	7.50452	+	23.0965i	0.402864	+	1.23989i	−0.519802	+	0.854287i	$0.673994\pi$
$348$	3.64203	+	2.64609i	0.195233	+	0.141845i
$349$	−2.68497	+	1.95074i	−0.143723	+	0.104421i	−0.657323	−	0.753609i	$-0.728311\pi$
$349$	−2.68497	+	1.95074i	−0.143723	+	0.104421i	0.513600	+	0.858030i	$0.328311\pi$
$350$	−0.0836570	+	0.257470i	−0.00447165	+	0.0137623i
$351$	−30.6269			−1.63474
$352$		0			0
$353$	20.3272			1.08191			0.540955	−	0.841051i	$-0.318063\pi$
$353$	20.3272			1.08191			0.540955	+	0.841051i	$0.318063\pi$
$354$	0.239366	−	0.736692i	0.0127221	−	0.0391548i
$355$	25.7887	−	18.7366i	1.36872	−	0.994436i
$356$	−10.4268	−	7.57553i	−0.552620	−	0.401502i
$357$	−1.73763	−	5.34787i	−0.0919650	−	0.283039i
$358$	0.335059	+	1.03121i	0.0177084	+	0.0545009i
$359$	23.4949	+	17.0700i	1.24001	+	0.900921i	0.997599	−	0.0692529i	$-0.0220615\pi$
$359$	23.4949	+	17.0700i	1.24001	+	0.900921i	0.242412	+	0.970173i	$0.422062\pi$
$360$	−28.2917	+	20.5552i	−1.49111	+	1.08335i
$361$	8.11414	−	24.9728i	0.427060	−	1.31436i
$362$	−1.62535			−0.0854264
$363$		0			0
$364$	−3.92246			−0.205593
$365$	−5.32499	+	16.3886i	−0.278723	+	0.857821i
$366$	−8.52572	+	6.19430i	−0.445647	+	0.323781i
$367$	18.4122	+	13.3773i	0.961111	+	0.698288i	0.953409	−	0.301682i	$-0.0975481\pi$
$367$	18.4122	+	13.3773i	0.961111	+	0.698288i	0.00770265	+	0.999970i	$0.497548\pi$
$368$	−1.47637	−	4.54380i	−0.0769611	−	0.236862i
$369$	−11.7855	−	36.2719i	−0.613527	−	1.88824i
$370$	−1.75070	−	1.27196i	−0.0910145	−	0.0661259i
$371$	0.539955	−	0.392300i	0.0280331	−	0.0203672i
$372$	−4.51852	+	13.9066i	−0.234274	+	0.721022i
$373$	22.2412			1.15160			0.575802	−	0.817589i	$-0.304690\pi$
$373$	22.2412			1.15160			0.575802	+	0.817589i	$0.304690\pi$
$374$		0			0
$375$	−36.3756			−1.87843
$376$	3.23238	−	9.94824i	0.166697	−	0.513041i
$377$	1.89030	−	1.37339i	0.0973556	−	0.0707330i
$378$	−6.56367	−	4.76878i	−0.337599	−	0.245280i
$379$	10.3430	+	31.8325i	0.531285	+	1.63513i	0.751543	+	0.659685i	$0.229310\pi$
$379$	10.3430	+	31.8325i	0.531285	+	1.63513i	−0.220258	+	0.975442i	$0.570690\pi$
$380$	−6.91426	−	21.2799i	−0.354694	−	1.09164i
$381$	44.6223	+	32.4200i	2.28607	+	1.66093i
$382$	6.88179	−	4.99992i	0.352103	−	0.255818i
$383$	−1.89919	+	5.84512i	−0.0970443	+	0.298672i	−0.987781	−	0.155848i	$-0.950189\pi$
$383$	−1.89919	+	5.84512i	−0.0970443	+	0.298672i	0.890737	+	0.454520i	$0.150189\pi$
$384$	34.4486			1.75795
$385$		0			0
$386$	−1.17829			−0.0599733
$387$	17.8653	−	54.9838i	0.908145	−	2.79498i
$388$	10.6886	−	7.76572i	0.542631	−	0.394245i
$389$	−5.98967	−	4.35175i	−0.303689	−	0.220643i	0.425495	−	0.904961i	$-0.360100\pi$
$389$	−5.98967	−	4.35175i	−0.303689	−	0.220643i	−0.729184	+	0.684318i	$0.760100\pi$
$390$	3.52202	+	10.8397i	0.178344	+	0.548887i
$391$	−1.75119	−	5.38962i	−0.0885617	−	0.272565i
$392$	−1.92429	−	1.39808i	−0.0971915	−	0.0706138i
$393$	17.0838	−	12.4121i	0.861765	−	0.626109i
$394$	−0.186898	+	0.575213i	−0.00941578	+	0.0289788i
$395$	−8.69662			−0.437575
$396$		0			0
$397$	17.8079			0.893752			0.446876	−	0.894596i	$-0.352537\pi$
$397$	17.8079			0.893752			0.446876	+	0.894596i	$0.352537\pi$
$398$	3.23473	−	9.95549i	0.162143	−	0.499024i
$399$	17.0885	−	12.4155i	0.855494	−	0.621553i
$400$	0.493749	+	0.358729i	0.0246874	+	0.0179365i
$401$	7.93520	+	24.4220i	0.396265	+	1.21958i	0.927972	+	0.372650i	$0.121551\pi$
$401$	7.93520	+	24.4220i	0.396265	+	1.21958i	−0.531707	+	0.846929i	$0.678449\pi$
$402$	0.586217	+	1.80419i	0.0292378	+	0.0899848i
$403$	6.13987	+	4.46088i	0.305849	+	0.222212i
$404$	5.05455	−	3.67235i	0.251473	−	0.182706i
$405$	11.5667	−	35.5985i	0.574752	−	1.76890i
$406$	0.618957			0.0307183
$407$		0			0
$408$	13.3748			0.662152
$409$	−0.413324	+	1.27208i	−0.0204376	+	0.0629003i	−0.960755	−	0.277398i	$-0.910528\pi$
$409$	−0.413324	+	1.27208i	−0.0204376	+	0.0629003i	0.940318	+	0.340298i	$0.110528\pi$
$410$	−6.45955	+	4.69314i	−0.319014	+	0.231778i
$411$	−35.2256	−	25.5929i	−1.73755	−	1.26240i
$412$	8.45022	+	26.0071i	0.416312	+	1.28128i
$413$	0.113830	+	0.350331i	0.00560119	+	0.0172387i
$414$	−11.7585	−	8.54303i	−0.577897	−	0.419867i
$415$	−7.02646	+	5.10502i	−0.344915	+	0.250596i
$416$	4.50666	−	13.8701i	0.220957	−	0.680037i
$417$	−44.8068			−2.19420
$418$		0			0
$419$	37.4618			1.83013			0.915064	−	0.403310i	$-0.132140\pi$
$419$	37.4618			1.83013			0.915064	+	0.403310i	$0.132140\pi$
$420$	3.22698	−	9.93163i	0.157461	−	0.484614i
$421$	−6.68374	+	4.85602i	−0.325746	+	0.236668i	−0.738623	−	0.674118i	$-0.764524\pi$
$421$	−6.68374	+	4.85602i	−0.325746	+	0.236668i	0.412878	+	0.910787i	$0.364524\pi$
$422$	−8.00219	−	5.81393i	−0.389541	−	0.283018i
$423$	9.32003	+	28.6841i	0.453155	+	1.39467i
$424$	0.490564	+	1.50980i	0.0238239	+	0.0733224i
$425$	0.585659	+	0.425506i	0.0284086	+	0.0206401i
$426$	−25.2963	+	18.3788i	−1.22561	+	0.890458i
$427$	1.54863	−	4.76621i	0.0749437	−	0.230653i
$428$	−23.8980			−1.15515
$429$		0			0
$430$	−12.1034			−0.583679
$431$	−10.0914	+	31.0581i	−0.486085	+	1.49602i	0.344317	+	0.938853i	$0.388110\pi$
$431$	−10.0914	+	31.0581i	−0.486085	+	1.49602i	−0.830403	+	0.557164i	$0.811890\pi$
$432$	−14.7971	+	10.7507i	−0.711923	+	0.517243i
$433$	−12.7786	−	9.28422i	−0.614102	−	0.446171i	0.236754	−	0.971570i	$-0.423916\pi$
$433$	−12.7786	−	9.28422i	−0.614102	−	0.446171i	−0.850856	+	0.525398i	$0.823916\pi$
$434$	0.621256	+	1.91203i	0.0298212	+	0.0917803i
$435$	1.92226	+	5.91611i	0.0921654	+	0.283656i
$436$	23.7555	+	17.2594i	1.13768	+	0.826575i
$437$	17.2219	−	12.5124i	0.823834	−	0.598551i
$438$	5.22331	−	16.0757i	0.249580	−	0.768127i
$439$	20.6942			0.987678			0.493839	−	0.869553i	$-0.335593\pi$
$439$	20.6942			0.987678			0.493839	+	0.869553i	$0.335593\pi$
$440$		0			0
$441$	6.85818			0.326580
$442$	0.937107	−	2.88412i	0.0445737	−	0.137184i
$443$	−24.3477	+	17.6897i	−1.15680	+	0.840462i	−0.989370	−	0.145423i	$-0.953546\pi$
$443$	−24.3477	+	17.6897i	−1.15680	+	0.840462i	−0.167427	+	0.985885i	$0.553546\pi$
$444$	−5.93959	−	4.31537i	−0.281881	−	0.204798i
$445$	−5.50327	−	16.9373i	−0.260880	−	0.802906i
$446$	0.381922	+	1.17543i	0.0180845	+	0.0556584i
$447$	6.66256	+	4.84063i	0.315128	+	0.228954i
$448$	0.682474	−	0.495846i	0.0322438	−	0.0234265i
$449$	11.2465	−	34.6132i	0.530755	−	1.63350i	−0.221892	−	0.975071i	$-0.571223\pi$
$449$	11.2465	−	34.6132i	0.530755	−	1.63350i	0.752647	−	0.658424i	$-0.228777\pi$
$450$	1.85664			0.0875230
$451$		0			0
$452$	−2.60739			−0.122641
$453$	2.90064	−	8.92725i	0.136284	−	0.419439i
$454$	11.8878	−	8.63700i	0.557922	−	0.405354i
$455$	−4.38490	−	3.18582i	−0.205567	−	0.149353i
$456$	15.5254	+	47.7821i	0.727041	+	2.23760i
$457$	3.02652	+	9.31466i	0.141574	+	0.435721i	0.996555	−	0.0829393i	$-0.0264308\pi$
$457$	3.02652	+	9.31466i	0.141574	+	0.435721i	−0.854980	+	0.518661i	$0.826431\pi$
$458$	−10.9731	−	7.97243i	−0.512740	−	0.372527i
$459$	−17.5515	+	12.7519i	−0.819233	+	0.595208i
$460$	3.25217	−	10.0092i	0.151633	−	0.466680i
$461$	21.8596			1.01810			0.509052	−	0.860736i	$-0.329996\pi$
$461$	21.8596			1.01810			0.509052	+	0.860736i	$0.329996\pi$
$462$		0			0
$463$	6.75889			0.314112			0.157056	−	0.987590i	$-0.449800\pi$
$463$	6.75889			0.314112			0.157056	+	0.987590i	$0.449800\pi$
$464$	0.431193	−	1.32707i	0.0200176	−	0.0616079i
$465$	−16.3461	+	11.8762i	−0.758034	+	0.550744i
$466$	−11.4124	−	8.29161i	−0.528670	−	0.384102i
$467$	−9.27768	−	28.5538i	−0.429320	−	1.32131i	−0.898797	−	0.438366i	$-0.855558\pi$
$467$	−9.27768	−	28.5538i	−0.429320	−	1.32131i	0.469477	−	0.882945i	$-0.344442\pi$
$468$	8.31283	+	25.5843i	0.384261	+	1.18263i
$469$	−0.729838	−	0.530258i	−0.0337008	−	0.0244850i
$470$	5.10826	−	3.71136i	0.235626	−	0.171192i
$471$	10.9198	−	33.6077i	0.503157	−	1.54856i
$472$	−0.876166			−0.0403288
$473$		0			0
$474$	8.53056			0.391822
$475$	−0.840312	+	2.58622i	−0.0385562	+	0.118664i
$476$	−2.24786	+	1.63317i	−0.103031	+	0.0748561i
$477$	−3.70311	−	2.69046i	−0.169554	−	0.123188i
$478$	3.20720	+	9.87074i	0.146694	+	0.451477i
$479$	1.85519	+	5.70970i	0.0847659	+	0.260883i	0.984452	−	0.175655i	$-0.0562044\pi$
$479$	1.85519	+	5.70970i	0.0847659	+	0.260883i	−0.899686	+	0.436538i	$0.856204\pi$
$480$	31.4113	+	22.8217i	1.43372	+	1.04166i
$481$	−3.08280	+	2.23978i	−0.140563	+	0.102125i
$482$	2.91503	−	8.97153i	0.132776	−	0.408642i
$483$	9.93514			0.452064
$484$		0			0
$485$	18.2561			0.828965
$486$	−3.82450	+	11.7706i	−0.173483	+	0.533925i
$487$	−5.15120	+	3.74256i	−0.233423	+	0.169592i	−0.698348	−	0.715758i	$-0.746081\pi$
$487$	−5.15120	+	3.74256i	−0.233423	+	0.169592i	0.464925	+	0.885350i	$0.346081\pi$
$488$	9.64357	+	7.00646i	0.436544	+	0.317168i
$489$	−17.6613	−	54.3559i	−0.798671	−	2.45806i
$490$	−0.443681	−	1.36551i	−0.0200435	−	0.0616875i
$491$	10.0131	+	7.27496i	0.451886	+	0.328314i	0.790340	−	0.612669i	$-0.209904\pi$
$491$	10.0131	+	7.27496i	0.451886	+	0.328314i	−0.338454	+	0.940983i	$0.609904\pi$
$492$	−21.9153	+	15.9224i	−0.988019	+	0.717838i
$493$	0.511458	−	1.57411i	0.0230349	−	0.0708942i
$494$	11.3914			0.512525
$495$		0			0
$496$	4.53228			0.203505
$497$	4.59489	−	14.1416i	0.206109	−	0.634338i
$498$	6.89229	−	5.00754i	0.308851	−	0.224393i
$499$	11.5525	+	8.39337i	0.517160	+	0.375739i	0.815533	−	0.578711i	$-0.196444\pi$
$499$	11.5525	+	8.39337i	0.517160	+	0.375739i	−0.298373	+	0.954449i	$0.596444\pi$
$500$	5.55432	+	17.0944i	0.248397	+	0.764486i
$501$	−19.3381	−	59.5167i	−0.863965	−	2.65901i
$502$	−0.583701	−	0.424084i	−0.0260519	−	0.0189278i
$503$	4.79402	−	3.48306i	0.213755	−	0.155302i	−0.475756	−	0.879577i	$-0.657826\pi$
$503$	4.79402	−	3.48306i	0.213755	−	0.155302i	0.689511	+	0.724275i	$0.257826\pi$
$504$	−5.04086	+	15.5142i	−0.224538	+	0.691056i
$505$	8.63314			0.384170
$506$		0			0
$507$	−20.7473			−0.921419
$508$	8.42197	−	25.9202i	0.373665	−	1.15002i
$509$	−24.9772	+	18.1470i	−1.10709	+	0.804351i	−0.982204	−	0.187820i	$-0.939858\pi$
$509$	−24.9772	+	18.1470i	−1.10709	+	0.804351i	−0.124891	+	0.992171i	$0.539858\pi$
$510$	6.53162	+	4.74550i	0.289225	+	0.210134i
$511$	2.48393	+	7.64474i	0.109883	+	0.338184i
$512$	−4.91089	−	15.1142i	−0.217033	−	0.667958i
$513$	−65.9303	−	47.9012i	−2.91090	−	2.11489i
$514$	7.08774	−	5.14955i	0.312627	−	0.227137i
$515$	−11.6765	+	35.9365i	−0.514527	+	1.58355i
$516$	−41.0633			−1.80771
$517$		0			0
$518$	−1.00942			−0.0443516
$519$	−5.81183	+	17.8870i	−0.255111	+	0.785151i
$520$	10.4297	−	7.57765i	0.457374	−	0.332302i
$521$	−15.2799	−	11.1015i	−0.669423	−	0.486365i	0.200409	−	0.979712i	$-0.435773\pi$
$521$	−15.2799	−	11.1015i	−0.669423	−	0.486365i	−0.869832	+	0.493348i	$0.835773\pi$
$522$	−1.31175	−	4.03716i	−0.0574138	−	0.176702i
$523$	2.45424	+	7.55337i	0.107316	+	0.330286i	0.990267	−	0.139180i	$-0.0444466\pi$
$523$	2.45424	+	7.55337i	0.107316	+	0.330286i	−0.882951	+	0.469466i	$0.844447\pi$
$524$	−8.44156	−	6.13315i	−0.368771	−	0.267928i
$525$	−1.02676	+	0.745981i	−0.0448113	+	0.0325573i
$526$	−1.98108	+	6.09712i	−0.0863790	+	0.265847i
$527$	5.37595			0.234180
$528$		0			0
$529$	−12.9873			−0.564665
$530$	−0.296122	+	0.911370i	−0.0128627	+	0.0395874i
$531$	2.04380	−	1.48491i	0.0886935	−	0.0644396i
$532$	−8.44386	−	6.13482i	−0.366088	−	0.265978i
$533$	4.34471	+	13.3716i	0.188190	+	0.579190i
$534$	5.39818	+	16.6139i	0.233602	+	0.718954i
$535$	−26.7155	−	19.4099i	−1.15501	−	0.839165i
$536$	1.73596	−	1.26125i	0.0749821	−	0.0544777i
$537$	−1.57076	+	4.83432i	−0.0677835	+	0.208616i
$538$	3.19370			0.137690
$539$		0			0
$540$	−40.2899			−1.73380
$541$	−2.34904	+	7.22960i	−0.100993	+	0.310825i	−0.988769	−	0.149451i	$-0.952249\pi$
$541$	−2.34904	+	7.22960i	−0.100993	+	0.310825i	0.887776	+	0.460276i	$0.152249\pi$
$542$	10.8650	−	7.89389i	0.466692	−	0.339072i
$543$	−6.16444	−	4.47873i	−0.264541	−	0.192201i
$544$	−3.19234	−	9.82501i	−0.136870	−	0.421244i
$545$	12.5381	+	38.5884i	0.537075	+	1.65295i
$546$	4.30117	+	3.12498i	0.184073	+	0.133737i
$547$	17.5548	−	12.7543i	0.750590	−	0.545335i	−0.145420	−	0.989370i	$-0.546453\pi$
$547$	17.5548	−	12.7543i	0.750590	−	0.545335i	0.896010	+	0.444035i	$0.146453\pi$
$548$	−6.64845	+	20.4618i	−0.284008	+	0.874086i
$549$	−34.3697			−1.46686
$550$		0			0
$551$	6.21726			0.264864
$552$	−7.30247	+	22.4747i	−0.310814	+	0.956587i
$553$	−3.28192	+	2.38446i	−0.139562	+	0.101397i
$554$	6.28660	+	4.56749i	0.267092	+	0.194054i
$555$	−3.13491	−	9.64827i	−0.133070	−	0.409546i
$556$	6.84170	+	21.0566i	0.290153	+	0.892999i
$557$	−32.8569	−	23.8719i	−1.39219	−	1.01149i	−0.995621	−	0.0934825i	$-0.970200\pi$
$557$	−32.8569	−	23.8719i	−1.39219	−	1.01149i	−0.396571	−	0.918004i	$-0.629800\pi$
$558$	11.1546	−	8.10430i	0.472212	−	0.343082i
$559$	−6.58604	+	20.2697i	−0.278560	+	0.857319i
$560$	−3.23681			−0.136780
$561$		0			0
$562$	8.08972			0.341244
$563$	7.24004	−	22.2825i	0.305131	−	0.939097i	−0.674497	−	0.738278i	$-0.735639\pi$
$563$	7.24004	−	22.2825i	0.305131	−	0.939097i	0.979628	−	0.200820i	$-0.0643606\pi$
$564$	17.3308	−	12.5915i	0.729757	−	0.530200i
$565$	−2.91479	−	2.11772i	−0.122626	−	0.0890931i
$566$	4.55177	+	14.0089i	0.191325	+	0.588838i
$567$	−5.39545	−	16.6055i	−0.226588	−	0.697365i
$568$	28.6130	+	20.7886i	1.20058	+	0.872269i
$569$	−9.01678	+	6.55107i	−0.378003	+	0.274635i	−0.760522	−	0.649313i	$-0.775057\pi$
$569$	−9.01678	+	6.55107i	−0.378003	+	0.274635i	0.382519	+	0.923948i	$0.375057\pi$
$570$	−9.37166	+	28.8430i	−0.392536	+	1.20810i
$571$	6.15846			0.257724			0.128862	−	0.991663i	$-0.458868\pi$
$571$	6.15846			0.257724			0.128862	+	0.991663i	$0.458868\pi$
$572$		0			0
$573$	39.8780			1.66593
$574$	−1.15092	+	3.54218i	−0.0480387	+	0.147848i
$575$	−1.03477	+	0.751805i	−0.0431529	+	0.0313524i
$576$	−4.68052	−	3.40060i	−0.195022	−	0.141692i
$577$	−4.47585	−	13.7752i	−0.186332	−	0.573471i	0.813637	−	0.581374i	$-0.197485\pi$
$577$	−4.47585	−	13.7752i	−0.186332	−	0.573471i	−0.999969	+	0.00790255i	$0.997485\pi$
$578$	2.85455	+	8.78540i	0.118734	+	0.365424i
$579$	−4.46888	−	3.24683i	−0.185720	−	0.134934i
$580$	2.48671	−	1.80670i	0.103255	−	0.0750192i
$581$	−1.25193	+	3.85305i	−0.0519389	+	0.159852i
$582$	−17.9075			−0.742288
$583$		0			0
$584$	−19.1192			−0.791159
$585$	−11.4866	+	35.3522i	−0.474914	+	1.46164i
$586$	−0.767891	+	0.557906i	−0.0317213	+	0.0230469i
$587$	−12.8285	−	9.32048i	−0.529491	−	0.384698i	0.290676	−	0.956821i	$-0.406120\pi$
$587$	−12.8285	−	9.32048i	−0.529491	−	0.384698i	−0.820167	+	0.572124i	$0.806120\pi$
$588$	−1.50528	−	4.63277i	−0.0620766	−	0.191052i
$589$	6.24035	+	19.2058i	0.257129	+	0.791362i
$590$	−0.427877	−	0.310871i	−0.0176154	−	0.0127984i
$591$	−2.29387	+	1.66660i	−0.0943573	+	0.0685546i
$592$	−0.703209	+	2.16426i	−0.0289017	+	0.0889503i
$593$	−22.9285			−0.941560			−0.470780	−	0.882251i	$-0.656027\pi$
$593$	−22.9285			−0.941560			−0.470780	+	0.882251i	$0.656027\pi$
$594$		0			0
$595$	−3.83934			−0.157397
$596$	1.25749	−	3.87015i	0.0515087	−	0.158527i
$597$	39.7012	−	28.8446i	1.62486	−	1.18053i
$598$	4.33475	+	3.14938i	0.177261	+	0.128788i
$599$	4.06395	+	12.5075i	0.166048	+	0.511044i	0.999112	−	0.0421329i	$-0.0134153\pi$
$599$	4.06395	+	12.5075i	0.166048	+	0.511044i	−0.833064	+	0.553177i	$0.813415\pi$
$600$	−0.932836	−	2.87097i	−0.0380829	−	0.117207i
$601$	22.1286	+	16.0774i	0.902645	+	0.655810i	0.939144	−	0.343524i	$-0.111621\pi$
$601$	22.1286	+	16.0774i	0.902645	+	0.655810i	−0.0364993	+	0.999334i	$0.511621\pi$
$602$	−4.56758	+	3.31854i	−0.186161	+	0.135254i
$603$	−1.91188	+	5.88415i	−0.0778576	+	0.239621i
$604$	−4.63819			−0.188725
$605$		0			0
$606$	−8.46830			−0.344001
$607$	14.4850	−	44.5801i	0.587926	−	1.80945i	0.000740345	−	1.00000i	$-0.499764\pi$
$607$	14.4850	−	44.5801i	0.587926	−	1.80945i	0.587186	−	0.809452i	$-0.300236\pi$
$608$	31.3946	−	22.8095i	1.27322	−	0.925049i
$609$	2.34751	+	1.70557i	0.0951260	+	0.0691131i
$610$	2.22350	+	6.84324i	0.0900270	+	0.277075i
$611$	−3.43582	−	10.5744i	−0.138999	−	0.427793i
$612$	15.4162	+	11.2005i	0.623164	+	0.452755i
$613$	−16.5601	+	12.0316i	−0.668857	+	0.485953i	−0.869642	−	0.493682i	$-0.835651\pi$
$613$	−16.5601	+	12.0316i	−0.668857	+	0.485953i	0.200786	+	0.979635i	$0.435651\pi$
$614$	6.09806	−	18.7679i	0.246098	−	0.757411i
$615$	−37.4312			−1.50937
$616$		0			0
$617$	44.1691			1.77818			0.889090	−	0.457733i	$-0.151338\pi$
$617$	44.1691			1.77818			0.889090	+	0.457733i	$0.151338\pi$
$618$	11.4535	−	35.2503i	0.460728	−	1.41798i
$619$	−0.551413	+	0.400625i	−0.0221632	+	0.0161025i	−0.598812	−	0.800890i	$-0.704360\pi$
$619$	−0.551413	+	0.400625i	−0.0221632	+	0.0161025i	0.576649	+	0.816992i	$0.304360\pi$
$620$	8.07705	+	5.86832i	0.324382	+	0.235677i
$621$	−11.8451	−	36.4554i	−0.475327	−	1.46291i
$622$	−5.56287	−	17.1208i	−0.223051	−	0.686480i
$623$	−6.72072	−	4.88289i	−0.269260	−	0.195629i
$624$	9.69651	−	7.04492i	0.388171	−	0.282023i
$625$	−7.05039	+	21.6989i	−0.282016	+	0.867955i
$626$	3.00896			0.120262
$627$		0			0
$628$	−17.4610			−0.696770
$629$	−0.834110	+	2.56713i	−0.0332582	+	0.102358i
$630$	−7.96627	+	5.78783i	−0.317384	+	0.230593i
$631$	29.8299	+	21.6727i	1.18751	+	0.862776i	0.992999	−	0.118124i	$-0.0376880\pi$
$631$	29.8299	+	21.6727i	1.18751	+	0.862776i	0.194511	+	0.980900i	$0.437688\pi$
$632$	−2.98172	−	9.17679i	−0.118606	−	0.365033i
$633$	−14.3292	−	44.1009i	−0.569536	−	1.75285i
$634$	−5.93312	−	4.31066i	−0.235634	−	0.171198i
$635$	30.4672	−	22.1357i	1.20906	−	0.878430i
$636$	−1.00465	+	3.09201i	−0.0398371	+	0.122606i
$637$	−2.52826			−0.100173
$638$		0			0
$639$	−101.977			−4.03414
$640$	7.26835	−	22.3697i	0.287307	−	0.884239i
$641$	16.5951	−	12.0570i	0.655466	−	0.476224i	−0.209663	−	0.977774i	$-0.567237\pi$
$641$	16.5951	−	12.0570i	0.655466	−	0.476224i	0.865129	+	0.501550i	$0.167237\pi$
$642$	26.2054	+	19.0393i	1.03424	+	0.751422i
$643$	−2.35984	−	7.26283i	−0.0930629	−	0.286418i	0.893681	−	0.448703i	$-0.148114\pi$
$643$	−2.35984	−	7.26283i	−0.0930629	−	0.286418i	−0.986744	+	0.162284i	$0.948114\pi$
$644$	−1.51703	−	4.66894i	−0.0597793	−	0.183982i
$645$	−45.9045	−	33.3516i	−1.80749	−	1.31322i
$646$	6.52815	−	4.74298i	0.256846	−	0.186610i
$647$	4.53724	−	13.9642i	0.178377	−	0.548989i	−0.821394	−	0.570361i	$-0.806803\pi$
$647$	4.53724	−	13.9642i	0.178377	−	0.548989i	0.999772	+	0.0213717i	$0.00680336\pi$
$648$	41.5297			1.63144
$649$		0			0
$650$	−0.684450			−0.0268463
$651$	−2.91246	+	8.96363i	−0.114148	+	0.351312i
$652$	−22.8473	+	16.5996i	−0.894770	+	0.650089i
$653$	−0.911790	−	0.662454i	−0.0356811	−	0.0259238i	0.569802	−	0.821782i	$-0.307020\pi$
$653$	−0.911790	−	0.662454i	−0.0356811	−	0.0259238i	−0.605483	+	0.795858i	$0.707020\pi$
$654$	−12.2987	−	37.8516i	−0.480918	−	1.48011i
$655$	−4.45545	−	13.7125i	−0.174089	−	0.535790i
$656$	6.79283	+	4.93528i	0.265215	+	0.192690i
$657$	44.5988	−	32.4029i	1.73996	−	1.26416i
$658$	0.910159	−	2.80118i	0.0354817	−	0.109201i
$659$	−10.0215			−0.390384			−0.195192	−	0.980765i	$-0.562533\pi$
$659$	−10.0215			−0.390384			−0.195192	+	0.980765i	$0.562533\pi$
$660$		0			0
$661$	15.7371			0.612101			0.306050	−	0.952015i	$-0.400992\pi$
$661$	15.7371			0.612101			0.306050	+	0.952015i	$0.400992\pi$
$662$	−3.41956	+	10.5243i	−0.132905	+	0.409040i
$663$	11.5015	−	8.35632i	0.446681	−	0.324533i
$664$	−7.79597	−	5.66410i	−0.302542	−	0.219810i
$665$	−4.45666	−	13.7162i	−0.172822	−	0.531891i
$666$	2.13927	+	6.58398i	0.0828949	+	0.255124i
$667$	2.36584	+	1.71888i	0.0916056	+	0.0665554i
$668$	−25.0166	+	18.1756i	−0.967920	+	0.703235i
$669$	−1.79046	+	5.51046i	−0.0692230	+	0.213047i
$670$	1.29526			0.0500403
$671$		0			0
$672$	18.1113			0.698657
$673$	−9.89226	+	30.4452i	−0.381319	+	1.17358i	0.557797	+	0.829977i	$0.311647\pi$
$673$	−9.89226	+	30.4452i	−0.381319	+	1.17358i	−0.939116	+	0.343601i	$0.888353\pi$
$674$	6.56743	−	4.77152i	0.252968	−	0.183792i
$675$	3.96140	+	2.87813i	0.152474	+	0.110779i
$676$	3.16797	+	9.75001i	0.121845	+	0.375000i
$677$	4.74033	+	14.5892i	0.182186	+	0.560710i	0.999889	−	0.0149305i	$-0.00475269\pi$
$677$	4.74033	+	14.5892i	0.182186	+	0.560710i	−0.817703	+	0.575641i	$0.804753\pi$
$678$	2.85913	+	2.07728i	0.109804	+	0.0797775i
$679$	6.88945	−	5.00548i	0.264393	−	0.192093i
$680$	2.82197	−	8.68512i	0.108218	−	0.333059i
$681$	68.8864			2.63973
$682$		0			0
$683$	1.04764			0.0400868			0.0200434	−	0.999799i	$-0.493620\pi$
$683$	1.04764			0.0400868			0.0200434	+	0.999799i	$0.493620\pi$
$684$	−22.1194	+	68.0766i	−0.845758	+	2.60298i
$685$	−24.0514	+	17.4743i	−0.918955	+	0.667660i
$686$	−0.541834	−	0.393666i	−0.0206873	−	0.0150302i
$687$	−19.6492	−	60.4739i	−0.749663	−	2.30722i
$688$	3.93314	+	12.1050i	0.149950	+	0.461497i
$689$	1.36515	+	0.991838i	0.0520080	+	0.0377860i
$690$	−11.5404	+	8.38458i	−0.439335	+	0.319195i
$691$	9.01969	−	27.7597i	0.343125	−	1.05603i	−0.619455	−	0.785032i	$-0.712646\pi$
$691$	9.01969	−	27.7597i	0.343125	−	1.05603i	0.962580	−	0.270998i	$-0.0873537\pi$
$692$	9.29326			0.353277
$693$		0			0
$694$	−16.2648			−0.617404
$695$	−9.45384	+	29.0959i	−0.358605	+	1.10367i
$696$	−5.58369	+	4.05679i	−0.211649	+	0.153772i
$697$	8.05730	+	5.85397i	0.305192	+	0.221735i
$698$	−0.686867	−	2.11396i	−0.0259983	−	0.0800145i
$699$	−20.4358	−	62.8950i	−0.772954	−	2.37891i
$700$	0.507346	+	0.368609i	0.0191759	+	0.0139321i
$701$	10.3380	−	7.51100i	0.390461	−	0.283687i	−0.375183	−	0.926951i	$-0.622420\pi$
$701$	10.3380	−	7.51100i	0.390461	−	0.283687i	0.765644	+	0.643264i	$0.222420\pi$
$702$	6.33860	−	19.5082i	0.239235	−	0.736290i
$703$	−10.1394			−0.382415
$704$		0			0
$705$	29.6009			1.11483
$706$	−4.20697	+	12.9477i	−0.158332	+	0.487294i
$707$	3.25797	−	2.36705i	0.122528	−	0.0890221i
$708$	−1.45166	−	1.05469i	−0.0545567	−	0.0396377i
$709$	11.7646	+	36.2076i	0.441828	+	1.35981i	0.885925	+	0.463828i	$0.153524\pi$
$709$	11.7646	+	36.2076i	0.441828	+	1.35981i	−0.444098	+	0.895978i	$0.646476\pi$
$710$	6.59726	+	20.3043i	0.247591	+	0.762006i
$711$	22.5080	+	16.3530i	0.844116	+	0.613286i
$712$	15.9856	−	11.6142i	0.599087	−	0.435262i
$713$	−2.93520	+	9.03361i	−0.109924	+	0.338311i
$714$	3.76602			0.140940
$715$		0			0
$716$	2.51169			0.0938663
$717$	−15.0354	+	46.2742i	−0.561507	+	1.72814i
$718$	−15.7355	+	11.4325i	−0.587245	+	0.426658i
$719$	31.7696	+	23.0819i	1.18481	+	0.860811i	0.992706	−	0.120564i	$-0.0384703\pi$
$719$	31.7696	+	23.0819i	1.18481	+	0.860811i	0.192100	+	0.981375i	$0.438470\pi$
$720$	6.85975	+	21.1121i	0.255648	+	0.786803i
$721$	5.44668	+	16.7632i	0.202845	+	0.624293i
$722$	14.2274	+	10.3368i	0.529491	+	0.384697i
$723$	35.7773	−	25.9937i	1.33057	−	0.966716i
$724$	−1.16347	+	3.58080i	−0.0432401	+	0.133079i
$725$	−0.373562			−0.0138737
$726$		0			0
$727$	−28.4699			−1.05589			−0.527946	−	0.849278i	$-0.677037\pi$
$727$	−28.4699			−1.05589			−0.527946	+	0.849278i	$0.677037\pi$
$728$	1.85831	−	5.71929i	0.0688735	−	0.211971i
$729$	−4.56314	+	3.31531i	−0.169005	+	0.122789i
$730$	−9.33691	−	6.78366i	−0.345574	−	0.251074i
$731$	4.66529	+	14.3583i	0.172552	+	0.531060i
$732$	7.54368	+	23.2170i	0.278822	+	0.858127i
$733$	−2.42168	−	1.75946i	−0.0894470	−	0.0649870i	0.542163	−	0.840273i	$-0.317606\pi$
$733$	−2.42168	−	1.75946i	−0.0894470	−	0.0649870i	−0.631610	+	0.775286i	$0.717606\pi$
$734$	−12.3315	+	8.95935i	−0.455163	+	0.330696i
$735$	2.07999	−	6.40154i	0.0767215	−	0.236124i
$736$	18.2527			0.672802
$737$		0			0
$738$	25.5431			0.940254
$739$	15.6773	−	48.2498i	0.576700	−	1.77490i	−0.0536180	−	0.998562i	$-0.517075\pi$
$739$	15.6773	−	48.2498i	0.576700	−	1.77490i	0.630318	−	0.776337i	$-0.282925\pi$
$740$	−4.05544	+	2.94645i	−0.149081	+	0.108314i
$741$	43.2041	+	31.3896i	1.58714	+	1.15313i
$742$	0.138131	+	0.425123i	0.00507095	+	0.0156068i
$743$	0.118625	+	0.365089i	0.00435191	+	0.0133938i	0.953209	−	0.302312i	$-0.0977586\pi$
$743$	0.118625	+	0.365089i	0.00435191	+	0.0133938i	−0.948857	+	0.315706i	$0.897759\pi$
$744$	−18.1363	−	13.1768i	−0.664909	−	0.483085i
$745$	4.54907	−	3.30510i	0.166665	−	0.121089i
$746$	−4.60309	+	14.1668i	−0.168531	+	0.518685i
$747$	27.7848			1.01659
$748$		0			0
$749$	−15.4037			−0.562840
$750$	7.52839	−	23.1700i	0.274898	−	0.846048i
$751$	31.8404	−	23.1334i	1.16187	−	0.844151i	0.171861	−	0.985121i	$-0.445022\pi$
$751$	31.8404	−	23.1334i	1.16187	−	0.844151i	0.990014	+	0.140970i	$0.0450221\pi$
$752$	−5.37182	−	3.90285i	−0.195890	−	0.142322i
$753$	−1.04521	−	3.21683i	−0.0380897	−	0.117228i
$754$	0.483576	+	1.48830i	0.0176108	+	0.0542005i
$755$	−5.18502	−	3.76714i	−0.188702	−	0.137100i
$756$	−15.2046	+	11.0468i	−0.552984	+	0.401767i
$757$	3.51868	−	10.8294i	0.127889	−	0.393600i	−0.866528	−	0.499129i	$-0.833653\pi$
$757$	3.51868	−	10.8294i	0.127889	−	0.393600i	0.994416	+	0.105528i	$0.0336534\pi$
$758$	−22.4168			−0.814214
$759$		0			0
$760$	34.3037			1.24433
$761$	2.31196	−	7.11547i	0.0838083	−	0.257936i	−0.900367	−	0.435130i	$-0.856702\pi$
$761$	2.31196	−	7.11547i	0.0838083	−	0.257936i	0.984176	+	0.177195i	$0.0567023\pi$
$762$	−29.8855	+	21.7131i	−1.08264	+	0.786582i
$763$	15.3119	+	11.1247i	0.554327	+	0.402742i
$764$	−6.08911	−	18.7403i	−0.220296	−	0.678002i
$765$	8.13668	+	25.0421i	0.294182	+	0.905400i
$766$	−3.33007	−	2.41944i	−0.120320	−	0.0874179i
$767$	−0.753447	+	0.547411i	−0.0272054	+	0.0197659i
$768$	−8.76652	+	26.9806i	−0.316335	+	0.973578i
$769$	26.8378			0.967798			0.483899	−	0.875124i	$-0.339220\pi$
$769$	26.8378			0.967798			0.483899	+	0.875124i	$0.339220\pi$
$770$		0			0
$771$	41.0714			1.47915
$772$	−0.843453	+	2.59588i	−0.0303565	+	0.0934278i
$773$	−3.61453	+	2.62611i	−0.130006	+	0.0944546i	−0.650888	−	0.759174i	$-0.725603\pi$
$773$	−3.61453	+	2.62611i	−0.130006	+	0.0944546i	0.520882	+	0.853629i	$0.325603\pi$
$774$	31.3253	+	22.7591i	1.12596	+	0.818060i
$775$	−0.374949	−	1.15398i	−0.0134686	−	0.0414520i
$776$	6.25926	+	19.2640i	0.224694	+	0.691538i
$777$	−3.82843	−	2.78152i	−0.137344	−	0.0997864i
$778$	4.01155	−	2.91456i	0.143821	−	0.104492i
$779$	−11.5607	+	35.5803i	−0.414206	+	1.27480i
$780$	26.4020			0.945342
$781$		0			0
$782$	3.79543			0.135724
$783$	3.45951	−	10.6473i	0.123633	−	0.380503i
$784$	−1.22150	+	0.887475i	−0.0436251	+	0.0316955i
$785$	−19.5196	−	14.1818i	−0.696685	−	0.506171i
$786$	4.37037	+	13.4506i	0.155886	+	0.479768i
$787$	4.16738	+	12.8259i	0.148551	+	0.457193i	0.997451	−	0.0713611i	$-0.0227343\pi$
$787$	4.16738	+	12.8259i	0.148551	+	0.457193i	−0.848899	+	0.528554i	$0.822734\pi$
$788$	1.13346	+	0.823508i	0.0403779	+	0.0293363i
$789$	−24.3145	+	17.6655i	−0.865620	+	0.628910i
$790$	1.79987	−	5.53944i	0.0640366	−	0.197084i
$791$	−1.68062			−0.0597560
$792$		0			0
$793$	12.6704			0.449937
$794$	−3.68556	+	11.3430i	−0.130796	+	0.402547i
$795$	−3.63442	+	2.64056i	−0.128900	+	0.0936512i
$796$	−19.6174	−	14.2529i	−0.695320	−	0.505179i
$797$	16.2250	+	49.9354i	0.574719	+	1.76880i	0.637134	+	0.770753i	$0.280120\pi$
$797$	16.2250	+	49.9354i	0.574719	+	1.76880i	−0.0624156	+	0.998050i	$0.519880\pi$
$798$	4.37156	+	13.4543i	0.154752	+	0.476277i
$799$	−6.37177	−	4.62936i	−0.225417	−	0.163775i
$800$	−1.88634	+	1.37050i	−0.0666921	+	0.0484546i
$801$	−17.6055	+	54.1843i	−0.622061	+	1.91451i
$802$	−17.1983			−0.607292
$803$		0			0
$804$	4.39443			0.154980
$805$	2.09623	−	6.45152i	0.0738822	−	0.227386i
$806$	−4.11214	+	2.98764i	−0.144844	+	0.105235i
$807$	12.1127	+	8.80038i	0.426387	+	0.309788i
$808$	2.95995	+	9.10980i	0.104131	+	0.320482i
$809$	0.398583	+	1.22671i	0.0140134	+	0.0431289i	0.957819	−	0.287373i	$-0.0927820\pi$
$809$	0.398583	+	1.22671i	0.0140134	+	0.0431289i	−0.943805	+	0.330502i	$0.892782\pi$
$810$	20.2811	+	14.7351i	0.712606	+	0.517738i
$811$	−27.6585	+	20.0951i	−0.971220	+	0.705633i	−0.955729	−	0.294247i	$-0.904931\pi$
$811$	−27.6585	+	20.0951i	−0.971220	+	0.705633i	−0.0154910	+	0.999880i	$0.504931\pi$
$812$	0.443068	−	1.36362i	0.0155486	−	0.0478538i
$813$	62.9596			2.20809
$814$		0			0
$815$	−39.0231			−1.36692
$816$	2.62358	−	8.07454i	0.0918436	−	0.282666i
$817$	−45.8801	+	33.3339i	−1.60514	+	1.16620i
$818$	−0.724728	−	0.526545i	−0.0253395	−	0.0184102i
$819$	5.35813	+	16.4906i	0.187228	+	0.576229i
$820$	5.71550	+	17.5905i	0.199594	+	0.614287i
$821$	32.0856	+	23.3115i	1.11979	+	0.813578i	0.984178	−	0.177184i	$-0.0566987\pi$
$821$	32.0856	+	23.3115i	1.11979	+	0.813578i	0.135616	+	0.990761i	$0.456699\pi$
$822$	23.5921	−	17.1407i	0.822870	−	0.597850i
$823$	−2.85134	+	8.77554i	−0.0993916	+	0.305896i	−0.988373	−	0.152047i	$-0.951414\pi$
$823$	−2.85134	+	8.77554i	−0.0993916	+	0.305896i	0.888982	+	0.457943i	$0.151414\pi$
$824$	−41.9241			−1.46049
$825$		0			0
$826$	−0.246707			−0.00858403
$827$	7.94043	−	24.4381i	0.276116	−	0.849797i	−0.712806	−	0.701361i	$-0.752576\pi$
$827$	7.94043	−	24.4381i	0.276116	−	0.849797i	0.988922	−	0.148436i	$-0.0474239\pi$
$828$	−27.2382	+	19.7897i	−0.946591	+	0.687739i
$829$	−8.84945	−	6.42950i	−0.307354	−	0.223306i	0.423406	−	0.905940i	$-0.360834\pi$
$829$	−8.84945	−	6.42950i	−0.307354	−	0.223306i	−0.730760	+	0.682634i	$0.760834\pi$
$830$	−1.79750	−	5.53215i	−0.0623923	−	0.192024i
$831$	11.2572	+	34.6461i	0.390508	+	1.20186i
$832$	1.72547	+	1.25363i	0.0598200	+	0.0434618i
$833$	−1.44888	+	1.05268i	−0.0502009	+	0.0364731i
$834$	9.27333	−	28.5404i	0.321109	−	0.988272i
$835$	−42.7282			−1.47867
$836$		0			0
$837$	36.3630			1.25689
$838$	−7.75317	+	23.8618i	−0.267829	+	0.824293i
$839$	28.1031	−	20.4181i	0.970228	−	0.704912i	0.0147243	−	0.999892i	$-0.495313\pi$
$839$	28.1031	−	20.4181i	0.970228	−	0.704912i	0.955503	+	0.294980i	$0.0953129\pi$
$840$	12.9524	+	9.41045i	0.446899	+	0.324691i
$841$	−8.69756	−	26.7684i	−0.299916	−	0.923047i
$842$	−1.70983	−	5.26232i	−0.0589247	−	0.181351i
$843$	30.6818	+	22.2916i	1.05674	+	0.767764i
$844$	−18.5369	+	13.4678i	−0.638065	+	0.463581i
$845$	−4.37749	+	13.4725i	−0.150590	+	0.463469i
$846$	−20.1996			−0.694478
$847$		0			0
$848$	1.00771			0.0346050
$849$	−21.3388	+	65.6740i	−0.732345	+	2.25393i
$850$	−0.392241	+	0.284980i	−0.0134538	+	0.00977474i
$851$	−3.85832	−	2.80323i	−0.132262	−	0.0960936i
$852$	22.3825	+	68.8863i	0.766813	+	2.36001i
$853$	6.37880	+	19.6319i	0.218406	+	0.672185i	0.998894	+	0.0470143i	$0.0149706\pi$
$853$	6.37880	+	19.6319i	0.218406	+	0.672185i	−0.780488	+	0.625171i	$0.785029\pi$
$854$	2.71539	+	1.97285i	0.0929189	+	0.0675095i
$855$	−80.0191	+	58.1373i	−2.73659	+	1.98825i
$856$	11.3220	−	34.8454i	0.386977	−	1.19099i
$857$	34.1512			1.16658			0.583291	−	0.812263i	$-0.301765\pi$
$857$	34.1512			1.16658			0.583291	+	0.812263i	$0.301765\pi$
$858$		0			0
$859$	−33.4493			−1.14127			−0.570637	−	0.821202i	$-0.693304\pi$
$859$	−33.4493			−1.14127			−0.570637	+	0.821202i	$0.693304\pi$
$860$	−8.66399	+	26.6650i	−0.295440	+	0.909269i
$861$	−14.1258	+	10.2630i	−0.481405	+	0.349761i
$862$	−17.6944	−	12.8557i	−0.602673	−	0.437868i
$863$	−10.5171	−	32.3683i	−0.358006	−	1.10183i	−0.954246	−	0.299022i	$-0.903340\pi$
$863$	−10.5171	−	32.3683i	−0.358006	−	1.10183i	0.596240	−	0.802806i	$-0.296660\pi$
$864$	−21.5930	−	66.4564i	−0.734609	−	2.26089i
$865$	10.3889	+	7.54799i	0.353234	+	0.256639i
$866$	8.55841	−	6.21805i	0.290827	−	0.211298i
$867$	−13.3822	+	41.1861i	−0.454483	+	1.39875i
$868$	4.65710			0.158072
$869$		0			0
$870$	−4.16619			−0.141247
$871$	0.704812	−	2.16919i	0.0238816	−	0.0735001i
$872$	−36.4202	+	26.4608i	−1.23334	+	0.896076i
$873$	−47.2491	−	34.3285i	−1.59914	−	1.16184i
$874$	4.40569	+	13.5593i	0.149025	+	0.458651i
$875$	3.58010	+	11.0184i	0.121029	+	0.372490i
$876$	−31.6773	−	23.0149i	−1.07028	−	0.777602i
$877$	6.36458	−	4.62414i	0.214917	−	0.156146i	−0.475119	−	0.879922i	$-0.657595\pi$
$877$	6.36458	−	4.62414i	0.214917	−	0.156146i	0.690035	+	0.723776i	$0.257595\pi$
$878$	−4.28291	+	13.1814i	−0.144541	+	0.444852i
$879$	−4.44971			−0.150085
$880$		0			0
$881$	13.3289			0.449063			0.224531	−	0.974467i	$-0.427915\pi$
$881$	13.3289			0.449063			0.224531	+	0.974467i	$0.427915\pi$
$882$	−1.41938	+	4.36841i	−0.0477931	+	0.147092i
$883$	13.8340	−	10.0510i	0.465552	−	0.338243i	−0.330153	−	0.943927i	$-0.607100\pi$
$883$	13.8340	−	10.0510i	0.465552	−	0.338243i	0.795705	+	0.605684i	$0.207100\pi$
$884$	−5.68318	−	4.12908i	−0.191146	−	0.138876i
$885$	−0.766184	−	2.35807i	−0.0257550	−	0.0792658i
$886$	−6.22863	−	19.1697i	−0.209255	−	0.644020i
$887$	−21.4539	−	15.5872i	−0.720351	−	0.523366i	0.166145	−	0.986101i	$-0.446868\pi$
$887$	−21.4539	−	15.5872i	−0.720351	−	0.523366i	−0.886496	+	0.462736i	$0.846868\pi$
$888$	9.10614	−	6.61600i	0.305582	−	0.222018i
$889$	5.42848	−	16.7071i	0.182065	−	0.560339i
$890$	11.9274			0.399808
$891$		0			0
$892$	2.86298			0.0958598
$893$	9.14231	−	28.1371i	0.305936	−	0.941573i
$894$	−4.46221	+	3.24199i	−0.149239	+	0.108428i
$895$	2.80781	+	2.03999i	0.0938548	+	0.0681895i
$896$	−3.39044	−	10.4347i	−0.113267	−	0.348599i
$897$	7.76209	+	23.8892i	0.259168	+	0.797639i
$898$	19.7197	+	14.3272i	0.658056	+	0.478106i
$899$	−2.24434	+	1.63061i	−0.0748529	+	0.0543838i
$900$	1.32904	−	4.09036i	0.0443013	−	0.136345i
$901$	1.19530			0.0398211
$902$		0			0
$903$	−26.4678			−0.880794
$904$	1.23528	−	3.80180i	0.0410848	−	0.126446i
$905$	−4.20896	+	3.05799i	−0.139911	+	0.101651i
$906$	5.08601	+	3.69521i	0.168972	+	0.122765i
$907$	2.73559	+	8.41928i	0.0908338	+	0.279558i	0.986146	−	0.165882i	$-0.0530472\pi$
$907$	2.73559	+	8.41928i	0.0908338	+	0.279558i	−0.895312	+	0.445440i	$0.853047\pi$
$908$	−10.5185	−	32.3726i	−0.349068	−	1.07432i
$909$	−22.3437	−	16.2337i	−0.741094	−	0.538436i
$910$	2.93676	−	2.13368i	0.0973526	−	0.0707308i
$911$	−17.2740	+	53.1639i	−0.572313	+	1.76140i	0.0728381	+	0.997344i	$0.476794\pi$
$911$	−17.2740	+	53.1639i	−0.572313	+	1.76140i	−0.645151	+	0.764055i	$0.723206\pi$
$912$	31.8921			1.05605
$913$		0			0
$914$	−6.55948			−0.216968
$915$	−10.4238	+	32.0812i	−0.344601	+	1.06057i
$916$	−25.4189	+	18.4679i	−0.839865	+	0.610197i
$917$	−5.44110	−	3.95319i	−0.179681	−	0.130546i
$918$	−4.49001	−	13.8188i	−0.148192	−	0.456090i
$919$	−14.9495	−	46.0098i	−0.493139	−	1.51772i	−0.819838	−	0.572596i	$-0.805936\pi$
$919$	−14.9495	−	46.0098i	−0.493139	−	1.51772i	0.326699	−	0.945128i	$-0.394064\pi$
$920$	13.0535	+	9.48392i	0.430361	+	0.312676i
$921$	74.8439	−	54.3773i	2.46619	−	1.79179i
$922$	−4.52412	+	13.9238i	−0.148994	+	0.458556i
$923$	37.5937			1.23741
$924$		0			0
$925$	0.609223			0.0200311
$926$	−1.39884	+	4.30517i	−0.0459686	+	0.141477i
$927$	97.7948	−	71.0521i	3.21200	−	2.33366i
$928$	4.31281	+	3.13344i	0.141575	+	0.102860i
$929$	0.267082	+	0.821994i	0.00876267	+	0.0269687i	0.955342	−	0.295502i	$-0.0954868\pi$
$929$	0.267082	+	0.821994i	0.00876267	+	0.0269687i	−0.946580	+	0.322470i	$0.895487\pi$
$930$	−4.18166	−	12.8698i	−0.137122	−	0.422018i
$931$	−5.44258	−	3.95427i	−0.178373	−	0.129596i
$932$	−26.4366	+	19.2073i	−0.865959	+	0.629156i
$933$	26.0789	−	80.2625i	0.853784	−	2.62768i
$934$	20.1079			0.657949
$935$		0			0
$936$	−41.2424			−1.34805
$937$	−16.5194	+	50.8416i	−0.539667	+	1.66092i	0.193678	+	0.981065i	$0.437958\pi$
$937$	−16.5194	+	50.8416i	−0.539667	+	1.66092i	−0.733344	+	0.679858i	$0.762042\pi$
$938$	0.488804	−	0.355137i	0.0159600	−	0.0115956i
$939$	11.4120	+	8.29134i	0.372418	+	0.270578i
$940$	−4.51985	−	13.9107i	−0.147421	−	0.453716i
$941$	−4.23353	−	13.0295i	−0.138009	−	0.424749i	0.858037	−	0.513588i	$-0.171684\pi$
$941$	−4.23353	−	13.0295i	−0.138009	−	0.424749i	−0.996046	+	0.0888397i	$0.971684\pi$
$942$	19.1469	+	13.9110i	0.623840	+	0.453246i
$943$	−14.2360	+	10.3431i	−0.463589	+	0.336817i
$944$	−0.171867	+	0.528952i	−0.00559379	+	0.0172159i
$945$	−25.9693			−0.844781
$946$		0			0
$947$	31.6444			1.02830			0.514152	−	0.857699i	$-0.328107\pi$
$947$	31.6444			1.02830			0.514152	+	0.857699i	$0.328107\pi$
$948$	6.10643	−	18.7936i	0.198328	−	0.610389i
$949$	−16.4413	+	11.9453i	−0.533707	+	0.387761i
$950$	−1.47341	−	1.07050i	−0.0478039	−	0.0347315i
$951$	−10.6242	−	32.6980i	−0.344514	−	1.06031i
$952$	−1.31635	−	4.05132i	−0.0426632	−	0.131304i
$953$	26.4856	+	19.2429i	0.857951	+	0.623338i	0.927327	−	0.374253i	$-0.122101\pi$
$953$	26.4856	+	19.2429i	0.857951	+	0.623338i	−0.0693755	+	0.997591i	$0.522101\pi$
$954$	2.48013	−	1.80192i	0.0802972	−	0.0583394i
$955$	8.41390	−	25.8953i	0.272268	−	0.837953i
$956$	24.0420			0.777573
$957$		0			0
$958$	−4.02083			−0.129907
$959$	−4.28533	+	13.1889i	−0.138381	+	0.425892i
$960$	−4.59371	+	3.33753i	−0.148261	+	0.107718i
$961$	17.7897	+	12.9250i	0.573862	+	0.416935i
$962$	−0.788639	−	2.42718i	−0.0254267	−	0.0782555i
$963$	32.6450	+	100.471i	1.05197	+	3.23763i
$964$	−17.6785	−	12.8442i	−0.569385	−	0.413683i
$965$	−3.05127	+	2.21688i	−0.0982238	+	0.0713637i
$966$	−2.05620	+	6.32833i	−0.0661571	+	0.203611i
$967$	32.3487			1.04026			0.520132	−	0.854086i	$-0.325883\pi$
$967$	32.3487			1.04026			0.520132	+	0.854086i	$0.325883\pi$
$968$		0			0
$969$	37.8287			1.21523
$970$	−3.77832	+	11.6285i	−0.121314	+	0.373367i
$971$	23.8069	−	17.2968i	0.764001	−	0.555079i	−0.136134	−	0.990690i	$-0.543468\pi$
$971$	23.8069	−	17.2968i	0.764001	−	0.555079i	0.900135	+	0.435611i	$0.143468\pi$
$972$	23.1941	+	16.8515i	0.743950	+	0.540511i
$973$	4.40990	+	13.5723i	0.141375	+	0.435107i
$974$	−1.31778	−	4.05570i	−0.0422243	−	0.129953i
$975$	−2.59591	−	1.88604i	−0.0831355	−	0.0604015i
$976$	6.12155	−	4.44757i	0.195946	−	0.142363i
$977$	4.23181	−	13.0242i	0.135388	−	0.416681i	−0.860262	−	0.509852i	$-0.829700\pi$
$977$	4.23181	−	13.0242i	0.135388	−	0.416681i	0.995650	+	0.0931709i	$0.0297003\pi$
$978$	38.2780			1.22399
$979$		0			0
$980$	−3.32595			−0.106244
$981$	40.1108	−	123.448i	1.28064	−	3.94141i
$982$	−6.70622	+	4.87236i	−0.214004	+	0.155483i
$983$	−13.7791	−	10.0111i	−0.439486	−	0.319305i	0.345945	−	0.938255i	$-0.387558\pi$
$983$	−13.7791	−	10.0111i	−0.439486	−	0.319305i	−0.785431	+	0.618950i	$0.787558\pi$
$984$	−12.8336	−	39.4979i	−0.409122	−	1.25915i
$985$	0.598240	+	1.84119i	0.0190615	+	0.0586653i
$986$	0.896797	+	0.651561i	0.0285598	+	0.0207499i
$987$	11.1707	−	8.11602i	0.355569	−	0.258336i
$988$	8.15432	−	25.0964i	0.259423	−	0.798423i
$989$	−26.6744			−0.848198
$990$		0			0
$991$	23.2202			0.737614			0.368807	−	0.929506i	$-0.379766\pi$
$991$	23.2202			0.737614			0.368807	+	0.929506i	$0.379766\pi$
$992$	−5.35072	+	16.4678i	−0.169886	+	0.522854i
$993$	−41.9696	+	30.4927i	−1.33187	+	0.967657i
$994$	8.05673	+	5.85356i	0.255544	+	0.185664i
$995$	−10.3540	−	31.8665i	−0.328245	−	1.01023i
$996$	−6.09839	−	18.7689i	−0.193235	−	0.594716i
$997$	−14.8678	−	10.8021i	−0.470868	−	0.342105i	0.326912	−	0.945055i	$-0.393992\pi$
$997$	−14.8678	−	10.8021i	−0.470868	−	0.342105i	−0.797779	+	0.602949i	$0.793992\pi$
$998$	−7.73720	+	5.62141i	−0.244917	+	0.177943i
$999$	−5.64193	+	17.3641i	−0.178503	+	0.549375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.x.372.2		16
11.2	odd	10		847.2.f.w.729.2		16
11.3	even	5		847.2.f.v.323.3		16
11.4	even	5		847.2.a.o.1.4		8
11.5	even	5	inner	847.2.f.x.148.2		16
11.6	odd	10		77.2.f.b.71.3	yes	16
11.7	odd	10		847.2.a.p.1.5		8
11.8	odd	10		847.2.f.w.323.2		16
11.9	even	5		847.2.f.v.729.3		16
11.10	odd	2		77.2.f.b.64.3	✓	16
33.17	even	10		693.2.m.i.379.2		16
33.26	odd	10		7623.2.a.cw.1.5		8
33.29	even	10		7623.2.a.ct.1.4		8
33.32	even	2		693.2.m.i.64.2		16
77.6	even	10		539.2.f.e.148.3		16
77.10	even	6		539.2.q.f.471.3		32
77.17	even	30		539.2.q.f.324.2		32
77.32	odd	6		539.2.q.g.471.3		32
77.39	odd	30		539.2.q.g.324.2		32
77.48	odd	10		5929.2.a.bs.1.4		8
77.54	even	6		539.2.q.f.361.2		32
77.61	even	30		539.2.q.f.214.3		32
77.62	even	10		5929.2.a.bt.1.5		8
77.65	odd	6		539.2.q.g.361.2		32
77.72	odd	30		539.2.q.g.214.3		32
77.76	even	2		539.2.f.e.295.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.3	✓	16	11.10	odd	2
77.2.f.b.71.3	yes	16	11.6	odd	10
539.2.f.e.148.3		16	77.6	even	10
539.2.f.e.295.3		16	77.76	even	2
539.2.q.f.214.3		32	77.61	even	30
539.2.q.f.324.2		32	77.17	even	30
539.2.q.f.361.2		32	77.54	even	6
539.2.q.f.471.3		32	77.10	even	6
539.2.q.g.214.3		32	77.72	odd	30
539.2.q.g.324.2		32	77.39	odd	30
539.2.q.g.361.2		32	77.65	odd	6
539.2.q.g.471.3		32	77.32	odd	6
693.2.m.i.64.2		16	33.32	even	2
693.2.m.i.379.2		16	33.17	even	10
847.2.a.o.1.4		8	11.4	even	5
847.2.a.p.1.5		8	11.7	odd	10
847.2.f.v.323.3		16	11.3	even	5
847.2.f.v.729.3		16	11.9	even	5
847.2.f.w.323.2		16	11.8	odd	10
847.2.f.w.729.2		16	11.2	odd	10
847.2.f.x.148.2		16	11.5	even	5	inner
847.2.f.x.372.2		16	1.1	even	1	trivial
5929.2.a.bs.1.4		8	77.48	odd	10
5929.2.a.bt.1.5		8	77.62	even	10
7623.2.a.ct.1.4		8	33.29	even	10
7623.2.a.cw.1.5		8	33.26	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.206962 + 0.636964i) q^{2} +(-2.54013 + 1.84551i) q^{3} +(1.25514 + 0.911915i) q^{4} +(0.662464 + 2.03885i) q^{5} +(-0.649815 - 1.99992i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.92429 + 1.39808i) q^{8} +(2.11929 - 6.52251i) q^{9} +O(q^{10})\)	\(q+(-0.206962 + 0.636964i) q^{2} +(-2.54013 + 1.84551i) q^{3} +(1.25514 + 0.911915i) q^{4} +(0.662464 + 2.03885i) q^{5} +(-0.649815 - 1.99992i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.92429 + 1.39808i) q^{8} +(2.11929 - 6.52251i) q^{9} -1.43578 q^{10} -4.87118 q^{12} +(-0.781276 + 2.40452i) q^{13} +(-0.541834 + 0.393666i) q^{14} +(-5.44548 - 3.95637i) q^{15} +(0.466573 + 1.43596i) q^{16} +(0.553425 + 1.70327i) q^{17} +(3.71599 + 2.69983i) q^{18} +(-5.44258 + 3.95427i) q^{19} +(-1.02778 + 3.16317i) q^{20} -3.13977 q^{21} -3.16429 q^{23} +(2.30778 - 7.10261i) q^{24} +(0.327016 - 0.237591i) q^{25} +(-1.36990 - 0.995290i) q^{26} +(3.74337 + 11.5209i) q^{27} +(0.479422 + 1.47551i) q^{28} +(-0.747669 - 0.543213i) q^{29} +(3.64707 - 2.64975i) q^{30} +(0.927602 - 2.85487i) q^{31} -5.76834 q^{32} -1.19946 q^{34} +(-0.662464 + 2.03885i) q^{35} +(8.60800 - 6.25408i) q^{36} +(1.21933 + 0.885898i) q^{37} +(-1.39232 - 4.28511i) q^{38} +(-2.45303 - 7.54965i) q^{39} +(-4.12526 - 2.99718i) q^{40} +(4.49897 - 3.26870i) q^{41} +(0.649815 - 1.99992i) q^{42} +8.42985 q^{43} +14.7024 q^{45} +(0.654888 - 2.01554i) q^{46} +(-3.55782 + 2.58491i) q^{47} +(-3.83525 - 2.78647i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.0836570 + 0.257470i) q^{50} +(-4.54917 - 3.30516i) q^{51} +(-3.17333 + 2.30556i) q^{52} +(0.206244 - 0.634755i) q^{53} -8.11314 q^{54} -2.37856 q^{56} +(6.52722 - 20.0887i) q^{57} +(0.500747 - 0.363814i) q^{58} +(0.298010 + 0.216517i) q^{59} +(-3.22698 - 9.93163i) q^{60} +(-1.54863 - 4.76621i) q^{61} +(1.62647 + 1.18170i) q^{62} +(5.54838 - 4.03113i) q^{63} +(0.260682 - 0.802296i) q^{64} -5.42003 q^{65} -0.902129 q^{67} +(-0.858607 + 2.64252i) q^{68} +(8.03770 - 5.83973i) q^{69} +(-1.16157 - 0.843932i) q^{70} +(-4.59489 - 14.1416i) q^{71} +(5.04086 + 15.5142i) q^{72} +(6.50301 + 4.72471i) q^{73} +(-0.816641 + 0.593325i) q^{74} +(-0.392186 + 1.20702i) q^{75} -10.4372 q^{76} +5.31654 q^{78} +(-1.25358 + 3.85813i) q^{79} +(-2.61863 + 1.90255i) q^{80} +(-14.1255 - 10.2628i) q^{81} +(1.15092 + 3.54218i) q^{82} +(1.25193 + 3.85305i) q^{83} +(-3.94087 - 2.86321i) q^{84} +(-3.10609 + 2.25670i) q^{85} +(-1.74466 + 5.36951i) q^{86} +2.90168 q^{87} -8.30727 q^{89} +(-3.04284 + 9.36491i) q^{90} +(-2.04541 + 1.48608i) q^{91} +(-3.97163 - 2.88556i) q^{92} +(2.91246 + 8.96363i) q^{93} +(-0.910159 - 2.80118i) q^{94} +(-11.6677 - 8.47707i) q^{95} +(14.6523 - 10.6455i) q^{96} +(2.63154 - 8.09904i) q^{97} -0.669744 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more